Geodesic
Convergences in JW-algebras and in their enveloping von Neumann algebras
Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 68-80.

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

We study properties of different convergences in JW-algebras with a faithful normal state. The relationship between these convergences and similar convergences in enveloping von Neumann algebras is established. Based on this, ergodic theorems are proved. 
@article{MT_2008_11_1_a3,
     author = {A. K. Karimov},
     title = {Convergences in {JW-algebras} and in their enveloping von {Neumann} algebras},
     journal = {Matemati\v{c}eskie trudy},
     pages = {68--80},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2008_11_1_a3/}
}
TY  - JOUR
AU  - A. K. Karimov
TI  - Convergences in JW-algebras and in their enveloping von Neumann algebras
JO  - Matematičeskie trudy
PY  - 2008
SP  - 68
EP  - 80
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2008_11_1_a3/
LA  - ru
ID  - MT_2008_11_1_a3
ER  - 
%0 Journal Article
%A A. K. Karimov
%T Convergences in JW-algebras and in their enveloping von Neumann algebras
%J Matematičeskie trudy
%D 2008
%P 68-80
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2008_11_1_a3/
%G ru
%F MT_2008_11_1_a3
A. K. Karimov. Convergences in JW-algebras and in their enveloping von Neumann algebras. Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 68-80. http://geodesic.mathdoc.fr/item/MT_2008_11_1_a3/

[1] Ayupov Sh. A., “Statisticheskie ergodicheskie teoremy v iordanovykh algebrakh”, Uspekhi mat. nauk, 36:6(222) (1981), 201–202 | MR | Zbl

[2] Ayupov Sh. A., “Ergodicheskie teoremy dlya markovskikh operatorov v iordanovykh algebrakh. I”, Izv. AN UzSSR. Ser. fiz.-mat. nauk, 1982, no. 3, 12–15 | MR | Zbl

[3] Ayupov Sh. A., “Ergodicheskie teoremy dlya markovskikh operatorov v iordanovykh algebrakh. II”, Izv. AN UzSSR. Ser. fiz.-mat. nauk, 1982, no. 5, 7–12 | MR | Zbl

[4] Ayupov Sh. A., Klassifikatsiya i predstavlenie uporyadochennykh iordanovykh algebr, Fan, Tashkent, 1986 | MR | Zbl

[5] Ganiev I. G., Karimov A. K., “Svoistva skhodimosti po mere na iordanovykh algebrakh”, Vladikavkazskii mat. zhurn., 5:4 (2003), 43–49 | MR | Zbl

[6] Goldshtein M. Sh., “Teoremy skhodimosti pochti vsyudu v algebrakh fon Neimana”, J. Operator Theory, 6 (1981), 223–311 | MR

[7] Karimov A. K., “O svoistvakh skhodimosti po mere v iordanovykh algebrakh”, Matematicheskii analiz i geometriya, Nauchnye trudy TashGU, TashGU, Tashkent, 1983, 38–41

[8] Karimov A. K., “Skhodimost pochti vsyudu v $JW$-algebrakh i ikh prilozheniya k usilennym zakonam bolshikh chisel”, Dokl. AN UzSSR, 1985, no. 11, 4–6 | MR | Zbl

[9] Karimov A. K., “Subadditivnye mery na iordanovykh algebrakh”, Uzbekskii mat. zhurn., 1993, no. 4, 42–47 | MR

[10] Karimov A. K., Mukhamedov F. M., “Printsip Banakha i ego prilozheniya v iordanovykh algebrakh”, Dokl. NAN Ukrainy, 2003, no. 1, 22–24 | MR | Zbl

[11] Karimov A. K., Mukhamedov F. M., “Individualnaya ergodicheskaya teorema otnositelno ravnomernoi posledovatelnosti i printsip Banakha v iordanovykh algebrakh”, Mat. sb., 194:2 (2003), 73–86 | MR | Zbl

[12] Sinai Ya. G., Anshelevich V. V., “Nekotorye voprosy nekommutativnoi ergodicheskoi teorii”, Uspekhi mat. nauk, 31:4(190) (1976), 151–167 | MR | Zbl

[13] Egamberdiev O. I., Ergodicheskie svoistva absolyutnykh szhatii i invariantnost polozhitelnykh funktsionalov v $JBW$-algebrakh, Dis. ... kand. fiz.-mat. nauk, Tashkent, 1989

[14] Ayupov Sh. A., “Extensions of traces and type criterions for Jordan algebras of self-adjoint operators”, Math. Z., 181 (1982), 253–268 | DOI | MR | Zbl

[15] Batty C. J. K., “The strong laws of large numbers for states and traces of a $W^*$-algebra”, Z. Wahrsch. Verw. Gebiete, 48:2 (1979), 177–191 | DOI | MR | Zbl

[16] Goldstein M., Litvinov S., “Banach principle in the space of $\tau$-measurable operators”, Studia Math., 143:1 (2000), 33–41 | MR | Zbl

[17] Jajte R., Strong Limit Theorems in Noncommutative Probability, Lecture Notes in Math., 1110, Springer–Verlag, Berlin, 1985 | MR | Zbl

[18] Lance E. C., “Ergodic theorem for convex sets and operator algebras”, Invent. Math., 37:3 (1976), 201–214 | DOI | MR | Zbl

[19] Muratov M. A., Chilin V. I., “Almost-everywhere convergence and $(o)$-convergence in rings of measurable operators associated with a finite von Neumann algebra”, Ukrainian Math. J., 55:9 (2003), 1445–1456 | DOI | MR | Zbl

[20] Paszkiewicz A., “Convergences in $W^*$-algebras”, J. Funct. Anal., 69 (1986), 143–154 | DOI | MR | Zbl

[21] Petz D., “Quasi-uniform ergodic theorem in von Neumann algebras”, Bull. London Math. Soc., 16:2 (1984), 151–156 | DOI | MR | Zbl

[22] Størmer E., “On the Jordan structure of $C^*$-algebras”, Trans. Amer. Math. Soc., 120:12 (1965), 438–447 | MR

[23] Størmer E., “Jordan algebras of type I”, Acta Math., 115:3–4 (1966), 165–184 | MR

[24] Størmer E., “Irreducible Jordan algebras of self-adjoint operators”, Trans. Amer. Math. Soc., 130:1 (1968), 153–166 | DOI | MR

[25] Topping D. M., “Jordan algebras of self-adjoint operators”, Mem. Amer. Math. Soc., 53, 1965, 1–48 | MR

[26] Yeadon F. J., “Convergence of measurable operators”, Math. Proc. Cambridge Philos. Soc., 74 (1973), 257–268 | DOI | MR | Zbl

[27] Yeadon F. J., “Ergodic theorem for semifinite von Neumann algebras. I”, J. London Math. Soc. (2), 16:2 (1977), 326–332 | DOI | MR | Zbl

[28] Yeadon F. J., “Ergodic theorem for semifinite von Neumann algebras. II”, Math. Proc. Cambridge Philos. Soc., 88:1 (1980), 135–147 | DOI | MR | Zbl