The bundle convergence in von Neumann algebras and their L 2 -spaces

Ewa Hensz; Ryszard Jajte; Adam Paszkiewicz

Studia Mathematica (1996)

  • Volume: 120, Issue: 1, page 23-46
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Hensz, Ewa, Jajte, Ryszard, and Paszkiewicz, Adam. "The bundle convergence in von Neumann algebras and their $L_2$-spaces." Studia Mathematica 120.1 (1996): 23-46. <http://eudml.org/doc/216318>.

@article{Hensz1996,
abstract = {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.},
author = {Hensz, Ewa, Jajte, Ryszard, Paszkiewicz, Adam},
journal = {Studia Mathematica},
keywords = {bundle convergence; almost uniform convergence; von Neumann algebras; classical limit theorems},
language = {eng},
number = {1},
pages = {23-46},
title = {The bundle convergence in von Neumann algebras and their $L_2$-spaces},
url = {http://eudml.org/doc/216318},
volume = {120},
year = {1996},
}

TY - JOUR
AU - Hensz, Ewa
AU - Jajte, Ryszard
AU - Paszkiewicz, Adam
TI - The bundle convergence in von Neumann algebras and their $L_2$-spaces
JO - Studia Mathematica
PY - 1996
VL - 120
IS - 1
SP - 23
EP - 46
AB - 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.
LA - eng
KW - bundle convergence; almost uniform convergence; von Neumann algebras; classical limit theorems
UR - http://eudml.org/doc/216318
ER -

References

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  3. [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. [4] V. F. Gaposhkin, Individual ergodic theorem for normal operators in L 2 , Functional Anal. Appl. 15 (1981), 18-22. Zbl0457.47012
  5. [5] M. S. Goldstein, Theorems in almost everywhere convergence, J. Oper. Theory 6 (1981), 233-311 (in Russian). 
  6. [6] E. Hensz and R. Jajte, Pointwise convergence theorems in L 2 over a von Neumann algebra, Math. Z. 193 (1986), 413-429. Zbl0613.46056
  7. [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. Zbl0856.46034
  8. [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. Zbl0823.46063
  9. [9] R. Jajte, Strong limit theorems for orthogonal sequences in von Neumann algebras, Proc. Amer. Math. Soc. 94 (1985), 225-236. Zbl0601.46058
  10. [10] R. Jajte, Strong Limit Theorems in Noncommutative Probability, Lecture Notes Math. 1100, Springer, Berlin, 1985. Zbl0554.46033
  11. [11] R. Jajte, Strong Limit Theorems in Noncommutative L 2 -Spaces, Lecture Notes Math. 1477, Springer, Berlin, 1991. Zbl0743.46069
  12. [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. [13] B. Kümmerer, A non-commutative individual ergodic theorem, Invent. Math. 46 (1978), 139-145. Zbl0379.46060
  14. [14] E. C. Lance, Ergodic theorem for convex sets and operator algebras, ibid. 37 (1976), 201-214. Zbl0338.46054
  15. [15] D. Menchoff [D. Men'shov], Sur les séries de fonctions orthogonales, Fund. Math. 4 (1923), 82-105. Zbl49.0293.01
  16. [16] W. Orlicz, Zur Theorie der Orthogonalreihen, Bull. Internat. Acad. Polon. Sci. Sér. A 1927, 81-115. Zbl53.0265.05
  17. [17] A. Paszkiewicz, Convergence in W*-algebras, J. Funct. Anal. 69 (1986), 143-154. Zbl0612.46060
  18. [18] A. Paszkiewicz, A limit in probability in a W*-algebra is unique, ibid. 90 (1990), 429-444. Zbl0821.46081
  19. [19] D. Petz, Quasi-uniform ergodic theorems in von Neumann algebras, Bull. London Math. Soc. 16 (1984), 151-156. Zbl0535.46042
  20. [20] H. Rademacher, Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen, Math. Ann. 87 (1922), 112-138. Zbl48.0485.05
  21. [21] I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. 57 (1953), 401-457. Zbl0051.34201
  22. [22] Y. G. Sinai and V. V. Anshelevich, Some problems of non-commutative ergodic theory, Russian Math. Surveys 31 (1976), 157-174. Zbl0365.46053

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