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1996 | 120 | 1 | 23-46
Tytuł artykułu

The bundle convergence in von Neumann algebras and their $L_2$-spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A stronger version of almost uniform convergence in von Neumann algebras is introduced. This "bundle convergence" is additive and the limit is unique. Some extensions of classical limit theorems are obtained.
Słowa kluczowe
Czasopismo
Rocznik
Tom
120
Numer
1
Strony
23-46
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-08-13
poprawiono
1996-04-09
Twórcy
autor
  • Institute of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [1] G. Alexits, Convergence Problems of Orthogonal Series, Pergamon Press, New York, 1961.
  • [2] N. Dang-Ngoc, Pointwise convergence of martingales in von Neumann algebras, Israel J. Math. 34 (1979), 273-280.
  • [3] V. F. Gaposhkin, Criteria of the strong law of large numbers for some classes of stationary processes and homogeneous random fields, Theory Probab. Appl. 22 (1977), 295-319.
  • [4] V. F. Gaposhkin, Individual ergodic theorem for normal operators in $L_2$, Functional Anal. Appl. 15 (1981), 18-22.
  • [5] M. S. Goldstein, Theorems in almost everywhere convergence, J. Oper. Theory 6 (1981), 233-311 (in Russian).
  • [6] E. Hensz and R. Jajte, Pointwise convergence theorems in $L_2$ over a von Neumann algebra, Math. Z. 193 (1986), 413-429.
  • [7] E. Hensz, R. Jajte and A. Paszkiewicz, The unconditional pointwise convergence of orthogonal series in $L_2$ over a von Neumann algebra, Colloq. Math. 69 (1995), 167-178.
  • [8] E. Hensz, R. Jajte and A. Paszkiewicz, On the almost uniform convergence in noncommutative $L_2$-spaces, Probab. Math. Statist. 14 (1993), 347-358.
  • [9] R. Jajte, Strong limit theorems for orthogonal sequences in von Neumann algebras, Proc. Amer. Math. Soc. 94 (1985), 225-236.
  • [10] R. Jajte, Strong Limit Theorems in Noncommutative Probability, Lecture Notes Math. 1100, Springer, Berlin, 1985.
  • [11] R. Jajte, Strong Limit Theorems in Noncommutative $L_2$-Spaces, Lecture Notes Math. 1477, Springer, Berlin, 1991.
  • [12] R. Jajte, Asymptotic formula for normal operators in non-commutative $L_2$-space, in: Proc. Quantum Probability and Applications IV, Rome 1987, Lecture Notes in Math. 1396, Springer, 1989, 270-278.
  • [13] B. Kümmerer, A non-commutative individual ergodic theorem, Invent. Math. 46 (1978), 139-145.
  • [14] E. C. Lance, Ergodic theorem for convex sets and operator algebras, ibid. 37 (1976), 201-214.
  • [15] D. Menchoff [D. Men'shov], Sur les séries de fonctions orthogonales, Fund. Math. 4 (1923), 82-105.
  • [16] W. Orlicz, Zur Theorie der Orthogonalreihen, Bull. Internat. Acad. Polon. Sci. Sér. A 1927, 81-115.
  • [17] A. Paszkiewicz, Convergence in W*-algebras, J. Funct. Anal. 69 (1986), 143-154.
  • [18] A. Paszkiewicz, A limit in probability in a W*-algebra is unique, ibid. 90 (1990), 429-444.
  • [19] D. Petz, Quasi-uniform ergodic theorems in von Neumann algebras, Bull. London Math. Soc. 16 (1984), 151-156.
  • [20] H. Rademacher, Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen, Math. Ann. 87 (1922), 112-138.
  • [21] I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. 57 (1953), 401-457.
  • [22] Y. G. Sinai and V. V. Anshelevich, Some problems of non-commutative ergodic theory, Russian Math. Surveys 31 (1976), 157-174.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv120i1p23bwm
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