Representation theory for Banach algebras, Abelian groups, and semigroups in the spectral analysis of linear operators

A. G. Baskakov

Contemporary Mathematics. Fundamental Directions, Functional analysis. Functional analysis, Tome 9 (2004), pp. 3-151.

Bibliographie

[1] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR

[2] Baskakov A. G., “O pochti periodicheskikh funktsiyakh Levitana”, Sb. stud. rabot VGU, VGU, Voronezh, 1970, 91–94

[3] Baskakov A. G., Nekotorye voprosy teorii vektornykh pochti periodicheskikh funktsii, Disc. kand. fiz.-mat. nauk, VGU, Voronezh, 1973

[4] Baskakov A. G., “O spektralnom analize predstavlenii kommutativnykh banakhovykh algebr”, Tr. NII matematiki VGU, VGU, Voronezh, 1974, 1–6 | MR

[5] Baskakov A. G., “Spektralnyi sintez v kommutativnykh silno regulyarnykh banakhovykh algebrakh”, Tr. NII matematiki VGU, VGU, Voronezh, 1975, 3–7 | MR

[6] Baskakov A. G., K spektralnomu analizu v banakhovykh modulyakh nad kommutativnymi banakhovymi algebrami, Deponirovano v VINITI, # 3058-77, 1977

[7] Baskakov A. G., “Spektralnye kriterii pochti periodichnosti reshenii funktsionalnykh uravnenii”, Matem. zametki, 24:2 (1978), 195–206 | MR

[8] Baskakov A. G., “Spektralnye otobrazheniya banakhovykh modulei”, Metody resheniya operatornykh uravnenii, VGU, Voronezh, 1978, 7–12 | MR

[9] Baskakov A. G., “O spektralnykh funktorakh”, Shkola po teorii operatorov v funktsionalnykh prostranstvakh (Minsk, 1978), 17–18

[10] Baskakov A. G., “Lokalno regulyarnye kommutativnye banakhovy algebry”, Metody resheniya operatornykh uravnenii, VGU, Voronezh, 1979, 16–22 | MR

[11] Baskakov A. G., “Neravenstva bernshteinovskogo tipa v abstraktnom garmonicheskom analize”, Sib. matem. zhurn., 20:5 (1979), 942–952 | MR | Zbl

[12] Baskakov A. G., “Ob obschikh ergodicheskikh teoremakh v banakhovykh modulyakh”, Funkts. analiz i ego prilozh., 14:3 (1980), 63–64 | MR | Zbl

[13] Baskakov A. G., Zamena Krylova—Bogolyubova v teorii nelineinykh vozmuschenii lineinykh operatorov, Preprint 80-19, Institut matematiki AN USSR, Kiev, 1980, 44 pp. | MR

[14] Baskakov A. G., “Ob uslovii Ditkina v nekotorykh algebrakh Berlinga”, Izv. vyssh. uchebn. zav. Matematika., 1982, no. 1, 3–5 | MR | Zbl

[15] Baskakov A. G., “O dopolnyaemosti podprostranstv banakhovykh prostranstv”, VII shkola po teorii operatorov v funktsionalnykh prostranstvakh (Minsk, 1982), 20–21

[16] Baskakov A. G., “Metody abstraktnogo garmonicheskogo analiza v teorii vozmuschenii lineinykh operatorov”, Sib. matem. zhurn., 24:1 (1983), 21–39 | MR

[17] Baskakov A. G., “O spektralnom sinteze v banakhovykh modulyakh nad kommutativnymi banakhovymi algebrami”, Matem. zametki, 34:4 (1983), 573–585 | MR | Zbl

[18] Baskakov A. G., “Garmonicheskii analiz kosinusnoi i eksponentsialnoi operatornoi funktsii”, Matem. sbornik, 124:5 (1984), 68–95 | MR | Zbl

[19] Baskakov A. G., “Teorema o rasscheplenii operatora i nekotorye smezhnye voprosy analiticheskoi teorii vozmuschenii”, Izv. AN SSSR, ser. matem., 50:3 (1986), 435–457 | MR | Zbl

[20] Baskakov A. G., Garmonicheskii analiz lineinykh operatorov, Diss. dokt. fiz.-mat. nauk, Institut matematiki, Kiev, 1987

[21] Baskakov A. G., Garmonicheskii analiz lineinykh operatorov, VGU, Voronezh, 1987 | MR

[22] Baskakov A. G., “Operatornye ergodicheskie teoremy i dopolnyaemye podprostranstva banakhovykh prostranstv”, Izv. vyssh. uchebn. zav. Matematika, 1988, no. 11, 3–11 | MR | Zbl

[23] Baskakov A. G., “Diagonalizatsiya operatorov i dopolnyaemostpodprostranstv banakhovykh prostranstv”, Ukr. matem. zhurn., 42:7 (1990), 867–873 | MR | Zbl

[24] Baskakov A. G., “Spektr Berlinga v issledovanii nekotorykh klassovbanakhovykh algebr”, Usp. matem. nauk, 49:4 (1994.), 155–156 | MR | Zbl

[25] Baskakov A. G., “Lineinye differentsialnye operatory sneogranichennymi operatornymi koeffitsientami i polugruppyraznostnykh operatorov”, Matem. zametki, 59:6 (1996), 811–820 | MR | Zbl

[26] Baskakov A. G., “Polugruppy raznostnykh operatorov vspektralnom analize lineinykh differentsialnykh operatorov”, Funkts. analiz i ego prilozh., 30:3 (1996), 1–11 | MR | Zbl

[27] Baskakov A. G., Chernyshov K. I., “Uporyadochennye pary operatorov ipolugruppy”, Izv. RAEN. MMMIU, 2:3 (1998), 39–69

[28] Baskakov A. G., Chernyshov K. I., “Ob usloviyakh kompaktnostispektra uporyadochennykh par lineinykh operatorov”, Izv. RAEN. MMMIU, 3:3 (1999), 5–24 | MR | Zbl

[29] Baskakov A. G., Chernyshov K. I., “Postroenie fazovogo prostranstva i reshenii lineinykh uravnenii, ne razreshennykh otnositelno proizvodnoi”, Dokl. RAN, 371:3 (2000), 295–298 | MR | Zbl

[30] Baskakov A. G., Chernyshov K. I., “Spektralnaya teoriya lineinykhotnoshenii i vyrozhdennye polugruppy operatorov”, Matem. sbornik, 193:11 (2002), 3–42 | MR

[31] Boles Bosit R., “Obobschenie dvukh teorem M. I. Kadetsa o neopredelennom integrale abstraktnykh pochti periodicheskikh funktsii”, Matem. zametki, 9:3 (1971), 311–321 | MR | Zbl

[32] Bratteli U., Robinson D., Operatornye algebry i kvantovaya statisticheskaya mekhanika, Mir, M., 1982 | MR | Zbl

[33] Burbaki N., Spektralnaya teoriya, Mir, M., 1972 | MR | Zbl

[34] Gelfand I. M., Raikov D. A., Shilov G. E., Kommutativnye normirovannye koltsa, Fizmatgiz, M., 1960 | MR

[35] Gorin E. A., “Spektralnaya ustoichivost nekotorykh banakhovykh algebr”, Funkts. analiz i ego prilozh., 8:2 (1974), 93–94 | MR

[36] Gorin E. A., “Ob issledovaniyakh G. E. Shilova po teorii kommutativnykh banakhovykh algebr i ikh dalneishem razvitii”, Usp. matem. nauk, 33:4 (1978), 169–188 | MR | Zbl

[37] Gorin E. A., “Neravenstva Bernshteina s tochki zreniya operatorov”, Vestnik Kharkovskogo universiteta, prikl. matem. i mekh., 45 (1980), 77–105 | MR | Zbl

[38] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertove prostranstve, Nauka, M., 1967

[39] Grinlif F., Invariantnye srednie na topologicheskikh gruppakh, Mir, M., 1973

[40] Gurarii V. P., “Garmonicheskii analiz v prostranstvakh s vesom”, Tr. MMO, 35 (1976), 21–76 | MR

[41] Gurarii V. P., “Garmonicheskii analiz funktsii, ogranichennykh na pravoi poluosi i rastuschikh na levoi”, Zap. nauchn. sem. Lenigr. otd. matem. instituta AN SSSR, 113 (1981), 225–230 | MR | Zbl

[42] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR

[43] Danford N., Shvarts Dzh. T., Lineinye operatory, t. 1, IL, M., 1962 | MR | MR | Zbl

[44] Danford N., Shvarts Dzh. T., Lineinye operatory, t. 2, Mir, M., 1966 | MR | MR | Zbl

[45] Danford N., Shvarts Dzh. T., Lineinye operatory, t. 3, Mir, M., 1974 | MR | Zbl

[46] Ditkin V. V., “O nekotorykh spektralnykh svoistvakh puchka lineinykh ogranichennykh operatorov”, Matem. zametki, 31:1 (1982), 75–79 | MR | Zbl

[47] Dynkin E. M., “Operatornoe ischislenie, osnovannoe na formule Koshi—Grina, i kvazianalitichnost klassa $\alpha$”, Zap. nauchn. sem. Leningr. otd. matem. instituta AN SSSR, 19 (1970), 221–226 | MR

[48] Dynkin E. M., “Teoremy tipa Vinera—Levi i otsenki dlya operatorov Vinera—Khopfa”, Matem. issl., Kishinev, 8:3(29) (1973), 14–25 | MR

[49] Zhikov V. V., “Nekotorye voprosy dopustimosti i dikhotomii. Printsip usredneniya”, Izv. AN SSSR, seriya matem., 40:6 (1976), 1380–1408 | MR | Zbl

[50] Iosida K., Funktsionalnyi analiz, Mir, M., 1967 | MR

[51] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl

[52] Kakhan Zh. P., Absolyutno skhodyaschiesya ryady Fure, Mir, M., 1976

[53] Klement F., Kheimans Kh., Angenent S., van Duin K., de Pakhter B., Odnoparametricheskie polugruppy, Mir, M., 1992 | MR

[54] Krein S. G., Funktsionalnyi analiz, Sprav. matem. b-ka, Nauka, M., 1972 | MR | Zbl

[55] Krein S. G., Chernyshov K. I., “Singulyarno vozmuschennye differentsialnye uravneniya v banakhovom prostranstve”, IX Mezhdunarodnaya konf. po nelineinym kolebaniyam, t. 1, Nauk. dumka, Kiev, 1984, 193–197 | MR

[56] Kurbatov V. G., Lineinye differentsialno-raznostnye operatory, VGU, Voronezh, 1990

[57] Levitan B. M., “Ob odnom obobschenii neravenstv S. N. Bernshteina i H. Bohr'a”, Dokl. AN SSSR, 15:4 (1937), 251–253 | MR

[58] Levitan B. M., Pochti periodicheskie funktsii, Gostekhizdat, M., 1953

[59] Levitan B. M., Zhikov V. V., Pochti periodicheskie funktsii i differentsialnye uravneniya, MGU, M., 1978 | MR

[60] Lomonosov V. I., Nekotorye voprosy teorii invariantnykh podprostranstv, Diss. kand. fiz.-mat. nauk, Kharkov, 1973 | Zbl

[61] Lomonosov V. I., “Sovmestnyi approksimativnyi spektr kommutativnogo semeistva operatorov”, Teoriya funktsii, funkts. analiz i ikh prilozh., 32 (1979), 39–48 | MR

[62] Lomonosov V. I., Lyubich Yu. I., Matsaev V. I., “Dvoistvennost spektralnykh podprostranstv i usloviya otdelimosti spektra lineinogo operatora”, Dokl. AN SSSR, 216:4 (1974), 737–739 | MR | Zbl

[63] Lyubich Yu. I., “Ob usloviyakh polnoty sistemy sobstvennykh vektorov korrektnogo operatora”, Usp. matem. nauk, 18:1 (1963), 165–171 | MR | Zbl

[64] Lyubich Yu. I., “Ob odnom klasse operatorov v banakhovom prostranstve”, Usp. matem. nauk, 20:6 (1965), 131–133 | MR | Zbl

[65] Lyubich Yu. I., “O spektre predstavleniya topologicheskoi abelevoi gruppy”, Dokl. AN SSSR, 200:4 (1971), 777–780 | MR | Zbl

[66] Lyubich Yu. I., Matsaev V. I., “Ob operatorakh s otdelimym spektrom”, Matem. sbornik, 56:4 (1962), 433–468

[67] Lyubich Yu. I., Matsaev V. I., Feldman G. M., “O predstavleniyakh s otdelimym spektrom”, Funkts. analiz i ego prilozh., 7:2 (1973), 52–61 | MR | Zbl

[68] Lyubich Yu. I., Vvedenie v teoriyu banakhovykh predstavlenii grupp, Vischa shkola, Kharkov, 1985 | MR | Zbl

[69] Lyumis L., Vvedenie v abstraktnyi garmonicheskii analiz, IL, M., 1956

[70] Markus A. S., “Zadacha spektralnogo sinteza dlya operatorov s tochechnym spektrom”, Izv. AN SSSR, seriya matem., 34:3 (1970), 662–688 | MR | Zbl

[71] Markus A. S., Matsaev V. I., “O skhodimosti razlozhenii po sobstvennym vektoram operatora, blizkogo k samosopryazhennomu”, Lineinye operatory i integralnye uravneniya, Cb. nauchn. tr., Kishinev, 1981, 104–129 | MR | Zbl

[72] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

[73] Melnikova I. V., Gladchenko A. V., “Korrektnost zadachi Koshidlya vklyuchenii v banakhovykh prostranstvakh”, Dokl. RAN, 361:6 (1998), 736–739 | MR | Zbl

[74] Mukhamadiev E. M., “Ob obratimosti funktsionalnykh operatorov vprostranstve ogranichennykh na osi funktsii”, Matem. zametki, 11:3 (1972), 269–274 | Zbl

[75] Naimark M. A., Normirovannye koltsa, Nauka, M., 1968 | MR | Zbl

[76] Nikolskii N. K., Izbrannye zadachi vesovoi approksimatsii i spektralnogo analiza, Tr. MIAN, 70, 1974 | MR

[77] Nikolskii N. K., “Invariantnye podprostranstva v teorii operatorov i teorii funktsii”, Matematicheskii analiz, 12, VINITI, M., 1974, 199–412

[78] Nikolskii N. K., “Sovremennoe sostoyanie problemy spektralnogo analiza-sinteza”, Teoriya operatorov v funktsionalnykh prostranstvakh, Nauka, Sibirskoe otdelenie, Novosibirsk, 1977, 240–282

[79] Pich A., Operatornye idealy, Mir, M., 1982 | MR

[80] Radbel N. I., Uporyadochennye pary lineinykh operatorov i zadacha Koshidlya uravneniya $A\dot x(t)+Bx(t)=0$ v banakhovom prostranstve, Diss. kand. fiz.-mat. nauk, IPMiM, Donetsk, 1984

[81] Ritsner V. S., Teoriya lineinykh otnoshenii, Deponirovana v VINITI, No 846-82, 1982

[82] Rutkas A. G., “Zadacha Koshi dlya uravneniya $A\dot x(t)+Bx(t)=f(t)$”, Diff. ur-ya, 11:11 (1975), 1996–2010 | MR | Zbl

[83] Rudin U., Funktsionalnyi analiz, Mir, M., 1975 | MR

[84] Sviridyuk G. A., “K obschei teorii polugrupp operatorov”, Usp. matem. nauk, 49:4 (1994), 47–74 | MR | Zbl

[85] Sviridyuk G. A., Fedorov V. E., “O edinitsakh analiticheskikhpolugrupp operatorov s yadrami”, Sib. matem. zhurn., 39:3 (1998), 604–616 | MR

[86] Tyurin V. M., “Ob obratimosti lineinykh differentsialnykh operatorov vnekotorykh funktsionalnykh prostranstvakh”, Sib. matem. zhurn., 32:3 (1991), 160–165 | MR | Zbl

[87] Feis K., Algebra: koltsa, moduli i kategorii, t. 1, Mir, M., 1977

[88] Feldman G. M., “Ob izometricheskikh predstavleniyakh lokalno kompaktnykh abelevykh grupp”, Dokl. AN SSSR, 207:5 (1972), 1063–1066 | MR

[89] Feldman G. M., “O spektralnykh podprostranstvakh nekvazianaliticheskogo operatora”, Matem. fizika i funkts. analiz, Kharkov, 1972, no. 3, 81–87 | MR

[90] Feldman G. M., “O poluprostote algebry, porozhdennoi izometricheskim operatorom”, Funkts. analiz i ego prilozh., 8:2 (1974), 93–94 | MR

[91] Fedorov V. E., “Vyrozhdennye silno nepreryvnye polugruppy operatorov”, Algebra i analiz, 12:3 (2000), 173–200 | MR

[92] Khelemskii A. Ya., “Annulyatornye rasshireniya kommutativnykh banakhovykh algebr”, Izv. AN SSSR, seriya matem., 29:4 (1965), 945–956

[93] Khelemskii A. Ya., “O singulyarnykh rasshireniyakh algebry vsekh nepreryvnykh funktsii na kompakte”, Sib. matem. zhurn., 10:3 (1969), 671–684 | Zbl

[94] Khelemskii A.Ya., “Gomologicheskie metody v golomorfnom ischislenii ot neskolkikh operatorov v banakhovom prostranstve, po Teiloru”, Usp. matem. nauk, 36:1 (1981), 127–172 | MR | Zbl

[95] Khenri D., Geometricheskaya teoriya polulineinykh parabolicheskikhuravnenii, Mir, M., 1985 | MR

[96] Khille E., Fillips R.S., Funktsionalnyi analiz i polugruppy, IL, M., 1962

[97] Khyuitt E., Ross K., Abstraktnyi garmonicheskii analiz, t. 2, Nauka, M., 1975

[98] Chernyshov K. I., Ob operatornykh differentsialnykh uravneniyakh, ne razreshennykh otnositelno proizvodnoi, Diss. kand. fiz.-mat. nauk, IM AN USSR, Kiev, 1979

[99] Sheinberg M. V., “Gomologicheskie svoistva zamknutykh idealov, obladayuschikh ogranichennoi approksimativnoi edinitsei”, Vestnik MGU, mat.-mekh., 1972, no. 4, 39–45

[100] Shilov G. E., O regulyarnykh normirovannykh koltsakh, Tr. MIAN, 21, 1947 | MR | Zbl

[101] Shreider Yu. A., “Banakhovy funktsionaly i ergodicheskie teoremy”, Matem. zametki, 2:4 (1967), 385–394 | Zbl

[102] Shubin M. A., “Teoriya Favara–Mukhamadieva i psevdodifferentsialnye operatory”, Dokl. AN SSSR, 225:6 (1975), 46–48 | MR

[103] Edelshtein S., “Asimptoticheskoe rasscheplenie kraevykh zadach dlya abstraktnykh differentsialnykh uravnenii”, Sib. matem. zhurn., 35:6 (1994), 1401–1420 | MR

[104] Edvards E., Funktsionalnyi analiz, Mir, M., 1969

[105] Albrecht E., “Functionalkalküle in mehreren Veränderlichen für stetige Lineare Operatoren auf Banachräumen”, Manuscripta Math., 14 (1974), 1–40 | DOI | MR | Zbl

[106] Albrecht E., “Der Spectrale Abbiuldugsatz für nichtanalytische Functionalkalküle in mehreren Veränderlichen”, Manuscripta Math., 14 (1974), 263–277 | DOI | MR | Zbl

[107] Albrecht E., “An example of a weakly decomposable operator which is not decomposable”, Rev. Roum. Math. Pures Appl., 20 (1975), 855–861 | MR | Zbl

[108] Albrecht E., “On two questions of I. Colojoara and P. Foias”, Manuscripta Math., 25 (1978), 1–15 | DOI | MR | Zbl

[109] Albrecht E., Frunze S., “Non-analytic functional calculi in several variables”, Manuscripta Math., 18 (1976), 327–336 | DOI | MR | Zbl

[110] Albrecht E., “Spectral decomposition for systems of commuting operators”, Proc. Rog. Irish Acad. A, 81:1 (1981), 81–98 | MR

[111] Antoni P. D., Longo R., Zsido L., “A spectral mapping theorem for locally compact groups of operators”, Pacific. J. Math., 103 (1982), 17–24 | MR | Zbl

[112] Arendt W., “Spectral mapping theorems for compact and locally compact Abelian groups of operators”, Rend. Circ. Mat. Palermo, 29:1 (1981), 105–106 | MR

[113] Arendt W., Batty P. J. K., “Almost periodic solutions of first andsecond order Cauchy problems”, J. Differ. Equations, 137 (1997), 363–383 | DOI | MR | Zbl

[114] Arendt W., “Approximation of degenerate semigroups”, Tübinger Berichte fur Funktionalanalysis, 9 (1999/2000), 33–46 | MR

[115] Arendt W., Batty C., Hieber M., Neubrander, Vector-valued Laplace Transform and Cauchy Problems, Birkhäuser-Verlag, Basel, 2001 | MR | Zbl

[116] Arveson W., “On group of automorphisms of operator algebras”, J. Func. Anal., 15 (1974), 217–243 | DOI | MR | Zbl

[117] Atalla R. E., “On the ergodic theory of contractions”, Revista Colombina de Mathematicas, 10 (1976), 75–81 | MR | Zbl

[118] Atzmon A., “Operators which are annihilated by analytic functions and invariant subspaces”, Acta Math., 44:1:2 (1980), 27–63 | DOI | MR

[119] Bart H., Goldberg S., “Characterizations of almost periodic strongly continuous groups and semigroups”, Math. Ann., 236 (1978), 105–116 | DOI | MR | Zbl

[120] Basit B., “Harmonic Analysis and Asymptotic Behavior of Solutions of the Abstract Cauchy Problem”, Semigroup Forum, 54 (1997), 58–74 | DOI | MR | Zbl

[121] Bhatia R., Rosenthal P., “How and why to solve the operatorequation $AX-XB=Y$”, Bull. London Math. Soc., 29 (1997), 1–21 | DOI | MR | Zbl

[122] Batty P. J. K., Hutter W., Rabiger F., “Almost Periodicity of Mild Solutions of Inhomogeneous Periodic Cauchy Problems”, J. Differ. Equations, 156 (1999), 309–327 | DOI | MR | Zbl

[123] Beurling A., “Un theoreme sur les fonctions bornees et uniformement continues sur l'axe reel”, Acta Math., 77 (1945), 127–136 | DOI | MR | Zbl

[124] Bloom W., “Bernstein's inequality for locally compact abeliangroups”, J. Austral. Math. Soc., 17:1 (1974), 88–101 | DOI | MR | Zbl

[125] Bochner S., “Beiträge zur Theorie der fastperiodischen Functionen. I Teil”, Math. Ann., 96 (1926), 119–147 | DOI | MR | Zbl

[126] Bollobas Bela, “The spectral decomposition of compact Hermitian operators on Banach spaces”, Bull. London Math. Soc., 5:1 (1973), 29–36 | DOI | MR | Zbl

[127] De Boor C., “Dichotomies for band matrices”, SIAM. J. Numer. Anal., 17 (1980), 894–907 | DOI | MR | Zbl

[128] Bracic J., “Unital strong harmonic commutative Banach algebras”, Studia Math., 149:2 (2002), 253–266 | DOI | MR | Zbl

[129] Connes A., “Une classification des facteurs de type III”, Ann. Sci. Ecole Norm. Sup., 6 (1973), 133–152 | MR

[130] Colojoara I., Foias C., Theory of generalized spectral operators, Gordon and Breach, New York, 1968 | MR | Zbl

[131] Crabb B. J., Duncan J., “Some inequalities for norm unitaries in Banach algebras”, Proc. Edinburgh. Math. Soc., 21 (1978), 17–23 | DOI | MR | Zbl

[132] Cross R., Multivalued linear operators, M. Dekker, New York, 1998 | MR | Zbl

[133] Datry C., Muraz G., “Analyse harmonique dans les modules de Banach. Part I : Propriétés Generales”, Bull. Sci. Math. Paris, 119 (1995), 299–337 | MR | Zbl

[134] Datry C., Muraz G., “Analyse harmonique dans les modules de Banach. Part II : Presque-periodicites et ergadicites”, Bull. Sci. Math. Paris, 120 (1996), 493–536 | MR | Zbl

[135] Demko S., “Spectral bounds for $\|A^{-1}\|_\infty$”, J. Approxim. Theory, 48 (1986), 207–212 | DOI | MR | Zbl

[136] Domar Y., “Harmonic analysis based in certain commutative Banach algebras”, Acta Math., 96 (1956), 1–66 | DOI | MR | Zbl

[137] Domar Y., “Some results on norrow spectral analysis”, Math. Scand., 20 (1967), 5–18 | MR | Zbl

[138] Domar Y., Lindahl L.-A., “Three spectral notions for representations of commutative Banach algebras”, Ann. Inst. Fourier, 25:2 (1975), 1–32 | MR | Zbl

[139] Dowson H. R., Spectral theory of linear operators, Acad. Press, London, 1978 | MR | Zbl

[140] Dunkl S. F., “Modules over commutative Banach algebras”, Monatsch. für Math., 74 (1970), 6–14 | DOI | MR | Zbl

[141] Eberlein W. F., “Abstract ergodic theorems and weak almost periodic functions”, Trans. Amer. Math. Soc., 67 (1949), 217–240 | DOI | MR | Zbl

[142] Eberlein W. F., “Mean ergodic flows”, Adv. Math., 21:2 (1976), 229–232 | DOI | MR | Zbl

[143] Elmouloudi Ed-Dari, “On the $(C,\alpha)$-uniform ergodictheorem”, Studia Math., 156:1 (2003), 3–13 | DOI | MR | Zbl

[144] Engel K.J., Nagel R., One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, 2000 | MR

[145] Erdely I., Lange R., Spectral decomposition on Banach spaces, Lect. Notes Math., 623, Springer-Verlag, 1977 | MR | Zbl

[146] Favini A., Yagi A., Degenerate differential equations inBanach spaces, Pure and Applied Mathematics. A Series of Monographs and Textbooks, 215, M. Dekker, New York, 1998

[147] Favini A., Yagi A., “Multivalued linear operators anddegenerate evolution equations”, Ann. Math. Pure Appl., CLXIII (1993), 353–384 | DOI | MR | Zbl

[148] Fasangova E., “A Banach algebra approach to the weak spectral mapping theorem for $C_0$-groups”, Ulmer Seminare. Functionalanalysis und Differentialgleichungen, 5, 2000, 174–181

[149] Flaschka H., “Invariant Subspaces of Abstract Multiplication Operators”, Indiana University Math. J., 21:3 (1971), 413–418 | DOI | MR | Zbl

[150] Foias C., “Spectral maximal spaces and decomposable operators in Banach space”, Arc. Math., 14 (1963), 341–349 | DOI | MR | Zbl

[151] Frunza S., “The Taylor Spectrum and Spectral Decomposition”, J. Func. Anal., 19 (1975), 390–421 | DOI | MR | Zbl

[152] Gilbert J. E., “On projections of $L^\infty(G)$ on to translation-invariant subspaces”, Proc. London Math. Soc., 19:1 (1969), 69–88 | DOI | MR | Zbl

[153] Gindler H. A., Taylor A. E., “The minimum modules of a linear operator and its use in spectral theory”, Studia Math., 22 (1962/1963), 15–41 | MR | Zbl

[154] Gramain F., Meyer Y., “Ensembles de frequences et fonctions presque periodiques”, Colloq. Math., 30:2 (1974), 269–275 | MR | Zbl

[155] Hamza A. E., Muraz G., “Existence of Abstract Solutions ofintegro-differential operator equations”, Acta Math. Vietnamica, 28:1 (2003), 101–109 | MR | Zbl

[156] Hartman S., Ryll-Nardzewski C., “Über die Spaltung von Fourierreichen fastperiodische Functionen”, Studia Math., 19 (1960), 287–295 | MR | Zbl

[157] Herz S. S., “The spectral theory of bounded functionen”, Trans. Amer. Math. Soc., 94 (1960), 181–232 | DOI | MR | Zbl

[158] Huang S.-Z., Spectral theory for non-quasianalytic representations of locally compact Abelian groups, Ph. D. Thesis, Tubingen, 1995 | MR

[159] Huang S.-Z., “A spectral theory for locally compact abelian groups of automorphisms of commutative Banach algebras”, Studia Math., 132:1 (1999), 37–69 | MR | Zbl

[160] Jones L. K., Lin. M., “Unimodular eigenvalues and weak mixing”, J. Func. Anal., 35:1 (1980), 42–48 | DOI | MR | Zbl

[161] Koh K., “On a representation of a strongly harmonic ring bysheaves”, Pacific J. Math., 41 (1972), 459–468 | MR | Zbl

[162] Lange R., “Equivalent conditions for decomposable operators”, Proc. Amer. Math. Soc., 82:3 (1981), 401–406 | DOI | MR | Zbl

[163] Laursen K. B., Neumann M. M., An Introduction to Local Spectral Theory, London Mathematical Society Monographs, New Series, 20, Clarendon Press, Oxford, 2000 | MR | Zbl

[164] Leaf G., “A spectral theory for a class of linear operators”, Pacific J. Math., 13 (1963), 141–145 | MR

[165] Lehmann I., Rossberg H.-J., “Elementary Generalization of a Theorem of Pragmen-Lindelöf with Application”, Math. Nachr., 70 (1975), 87–93 | DOI | MR | Zbl

[166] Lloyd S. P., “On the mean ergodic theorem of Sine”, Proc. Amer. Math. Soc., 56 (1976), 121–126 | DOI | MR | Zbl

[167] Loomis L. H., “Spectral characterization of almost periodic functions”, Ann. Math., 72:2 (1960), 362–368 | DOI | MR | Zbl

[168] Lyubich Y. I., Introduction to the theory of Banach Representations of Groups, Birkhäuser-Verlag, 1988 | MR

[169] Mattila K., “On proper boundary points of the spectrum and complemented eigenspaces”, Math. Scand., 43 (1978), 363–368 | MR | Zbl

[170] Mayer A.E., “Gräste Polygone mit gegebenen Seitenvectoren”, Comm. Math. Helvetici, 10 (1938), 288–301 | DOI | Zbl

[171] Marshall E., “On the functional calcules of non-quasianalyticgroups of operators and cosine functions”, Rend. Circ. Math. Palermo, 35 (1986), 58–81 | DOI | MR

[172] Meyer Y., Algebraic numbers and harmonic analysis, North Holland, Amsterdam, 1972 | MR | Zbl

[173] Milne H., “Banach space properties of uniform algebras”, Bull. London Math. Soc., 4 (1972), 323–326 | DOI | MR | Zbl

[174] Mirkil H., “A counterexample to discrete spectral synthesis”, Composite Math., 14 (1960), 269–273 | MR | Zbl

[175] Nagel R. J., “Mittelergodische Halbgruppen linearer Operatoren”, Ann. Inst. Fourier (Grenoble), 23:4 (1973), 75–87 | MR | Zbl

[176] Nagel R., One Parameter Semigroups of Positive Operators, Lect. Notes Math., 1184, Springer-Verlag, 1986 | MR | Zbl

[177] Nagel R., Huang S.-Z., “Spectral mapping theorems for $C_0$-groups satisfying non-quasianalytic growth conditions”, Math. Nachr., 169 (1994), 207–218 | DOI | MR | Zbl

[178] Nagy B., “Operators with srectral decomposition property are decomposable”, Stud. Sci. Math. Hung., 13:3–4 (1978), 429–432 | MR | Zbl

[179] Fon Neumann J., “Über adjungierte Functionaloperatoren”, Ann. Math., 33 (1932), 294–310 | DOI

[180] Palmer T. W., Banach Algebras and the General Theory of *-Algebras. Vol. I: Algebras and Banach Algebras, Encyclopedia of Mathematics and its Applications, Cambridge Univ. Press, 1994 | MR | Zbl

[181] Palmer T. W., Banach Algebras and the General Theory of *-Algebras. Vol. II: *-Algebras, Encyclopedia of Mathematics and its Applications, Cambridge Univ. Press, 2002 | MR

[182] Olesen D., “On norm-continuity and compactness of spectrum”, Math. Scand., 35 (1974), 223–236 | MR

[183] Reiter H., Classical harmonic analysis and locally compact groups, Calderon Press, Oxford, 1968 | MR

[184] Romo J.G., “Spectral synthesis in Banach modules, I”, Tamkang J. Math., 11:1 (1980), 91–109 | MR | Zbl

[185] Romo Y.G., “Spectral synthesis in Banach modules, II”, Tamkang J. Math., 11:2 (1980), 191–201 | MR

[186] Rudin W., Fourier analysis on groups, Int. Publ., New York, 1962 | MR | Zbl

[187] Sato R., “On abstract mean ergodic theorems”, Tohoku Math. J., 30:4 (1978), 575–581 | DOI | MR

[188] Schwarz L., “Theorie generale des fonctions mogenne-periodiques”, Ann. Math., 48:4 (1947), 857–927 | DOI | MR

[189] Seferoglu H., “Spectral mapping theorem for representations ofmeasure algebras”, Proc. Edinb. Math. Soc., 40 (1997), 261–266 | DOI | MR | Zbl

[190] Seferoglu H., “A spectral mapping theorem for Banach modules”, Studia Math., 152:2 (2003), 99–103 | DOI | MR

[191] Sine R., “A mean ergodic theorem”, Proc. Amer. Math. Soc., 24:3 (1970), 438–439 | DOI | MR | Zbl

[192] Slodkowski Z., “An infinite family of joint spectra”, Studia Math., 61 (1977), 239–255 | MR | Zbl

[193] Slodkowski Z., Zelazko W., “On joint spectra of commuting families of operators”, Studia Math., 48 (1973), 83–88 | MR | Zbl

[194] Stampfli J.G., “A local theory for operators; Invariant subspaces”, Ind. Univ. Math. J., 22:2 (1972), 159–167 | DOI | MR | Zbl

[195] Takahasi S.-E., Inoue J., “A spectral mapping theorem for some representations of compact Abelian groups”, Proc. Edinb. Math. Soc., 35 (1992), 47–52 | DOI | MR | Zbl

[196] Taylor J.L., “A joint spectrum for several commuting operators”, J. Func. Anal., 6:2 (1970), 172–191 | DOI | MR | Zbl

[197] Taylor J.L., “The analytic functional calculus for several commuting operators”, Acta Math., 125 (1970), 1–38 | DOI | MR | Zbl

[198] Teleman S., “Analyse harmonique dans les algebras regylieres”, Rev. Roumaine Math. Pures Appl., 13 (1968), 691–750 | MR | Zbl

[199] Wermer J., “The existence of invariant subspace”, Duke Math. J., 19 (1952), 615–622 | DOI | MR | Zbl

[200] Zelazko W., “On a certain class of non-removable ideals in Banach algebras”, Studia Math., 44 (1972), 87–92 | MR | Zbl

[201] Zelazko W., “An axiomatic approach to joint spectra, I”, Studia Math., 64 (1979), 249–261 | MR | Zbl

[202] Zsido L., “On spectral subspaces associated to locally sompact abelian group of operators”, Adv. Math., 36 (1980), 213–276 | DOI | MR | Zbl