Geodesic
Fr\'echet Spaces with Unconditional Base
Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 29-32.

Voir la notice de l'article provenant de la source Math-Net.Ru

A nonnormable $\mathscr F$-space possessing an unconditional basis is not necessarily isomorphic to a generalized Köthe space.
Mots-clés : Fréchet space
Keywords: Köthe space, unconditional Schauder basis, Orlicz space, seminorm, Bernstein $n$-width. 
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M. M. Dragilev; P. A. Chalov. Fr\'echet Spaces with Unconditional Base. Matematičeskie zametki, Tome 80 (2006) no. 1, pp. 29-32. http://geodesic.mathdoc.fr/item/MZM_2006_80_1_a3/

[1] M. M. Dragilev, Bazisy v prostranstvakh Këte, RGU, Rostov-na-Donu, 1983, 2003

[2] A. Dynin, B. Mitiagin, “Criterion for nuclearity in terms of approximative dimension”, Bull. Acad. Polon. Sci. Ser. Math., 8:8 (1960), 535–540 | MR | Zbl

[3] G. Köthe, O. Toeplitz, “Lineare Räume mit unendlich vielen Koordinaten und Ringe unendlicher Matrizen”, J. Reine Angew. Math., 171 (1934), 251–270

[4] E. R. Lorch, “Bicontinuous linear transformation in certain vector spaces”, Bull. Amer. Math. Soc., 45:2 (1939), 564–569 | DOI | MR | Zbl

[5] I. M. Gelfand, “Zamechanie k rabote N. K. Bari «Biortogonalnye sistemy i bazisy v gilbertovom prostranstve»”, Uchen. zap. MGU. Ser. matem., 148 (1951), 224–225 | MR

[6] A. Pełczyński, “Projections in certain Banach spaces”, Studia Math., 19 (1960), 209–228 | MR

[7] J. Lindenstrauss, M. Zippin, “Banach spaces with a unique unconditional basis”, J. Funct. Anal., 3 (1969), 115–125 | DOI | MR | Zbl

[8] A. Pełczyński, J. Singer, “On non-equivalent bases and conditional bases in Banach spaces”, Studia Math., 25:1 (1964), 5–25 | MR

[9] W. Wojtinski, “On bases in certain countably Hilbert spaces”, Bull. Acad. Polon. Sci. Ser. Math., 14:12 (1966), 681–684 | MR

[10] J. Lindenstrauss, A. Pełczyński, “Absolutely summing operators in $L_p$ spaces and their applications”, Studia Math., 29 (1968), 275–326 | MR | Zbl

[11] V. P. Zakharyuta, “O kvaziekvivalentnosti bazisov v konechnykh tsentrakh gilbertovykh shkal”, Dokl. AN SSSR, 180:4 (1968), 786–788 | Zbl

[12] B. S. Mityagin, “Ekvivalentnost bazisov v gilbertovykh shkalakh”, Studia Math., 37:2 (1971), 111–137 | MR | Zbl

[13] V. P. Kondakov, Nekotorye voprosy izomorfizma i bazisov lokalno vypuklykh prostranstv, Diss. ... k.f.-m.n., RGU, Rostov-na-Donu, 1972

[14] N. J. Kalton, “On absolute bases”, Math. An., 200 (1973), 209–225 | DOI | MR | Zbl

[15] M. Zippin, “On perfectly homogeneous bases in Banach spaces”, Israel J. Math., 4 (1966), 265–272 | DOI | MR | Zbl

[16] V. P. Kondakov, Voprosy geometrii nenormiruemykh prostranstv, RGU, Rostov-na-Donu, 1983

[17] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces, I, II, Springer-Verlag, Berlin, Heidelberg, New York, 1977, 1979 | MR

[18] V. M. Tikhomirov, “Ob $n$-mernykh poperechnikakh nekotorykh funktsionalnykh klassov”, Dokl. AN SSSR, 130:4 (1960), 734–737 | Zbl

[19] V. M. Tikhomirov, “Poperechniki mnozhestv v funktsionalnom prostranstve i teoriya nailuchshikh priblizhenii”, UMN, 15:3 (1960), 81–120 | MR | Zbl

[20] V. M. Tikhomirov, Nekotorye voprosy teorii priblizhenii, MGU, M., 1976 | MR

[21] P. A. Chalov, “Poperechniki po Bernshteinu mnozhestv v koordinatnykh prostranstvakh Orlicha”, Teor. funkts., funkts. analiz i ikh prilozh., Resp. mezhved. nauch. sbornik, 35, Vischa shkola, Kharkov, 1981, 119–123 | MR

[22] B. S. Mityagin, “Approksimativnaya razmernost i bazisy v yadernykh prostranstvakh”, UMN, 16:4 (1961), 63–132 | MR | Zbl

[23] G. Metafune, V. B. Moscatelli, “On the space $\ell^{p+}=I_{q>p}\ell^q$”, Math. Nachr., 147 (1990), 7–12 | MR | Zbl