The bundle convergence in von Neumann algebras and their -spaces
Ewa Hensz; Ryszard Jajte; Adam Paszkiewicz
Studia Mathematica (1996)
- Volume: 120, Issue: 1, page 23-46
- ISSN: 0039-3223
Access Full Article
topAbstract
topHow to cite
topReferences
top- [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 , Functional Anal. Appl. 15 (1981), 18-22. Zbl0457.47012
- [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 over a von Neumann algebra, Math. Z. 193 (1986), 413-429. Zbl0613.46056
- [7] E. Hensz, R. Jajte and A. Paszkiewicz, The unconditional pointwise convergence of orthogonal series in over a von Neumann algebra, Colloq. Math. 69 (1995), 167-178. Zbl0856.46034
- [8] E. Hensz, R. Jajte and A. Paszkiewicz, On the almost uniform convergence in noncommutative -spaces, Probab. Math. Statist. 14 (1993), 347-358. Zbl0823.46063
- [9] R. Jajte, Strong limit theorems for orthogonal sequences in von Neumann algebras, Proc. Amer. Math. Soc. 94 (1985), 225-236. Zbl0601.46058
- [10] R. Jajte, Strong Limit Theorems in Noncommutative Probability, Lecture Notes Math. 1100, Springer, Berlin, 1985. Zbl0554.46033
- [11] R. Jajte, Strong Limit Theorems in Noncommutative -Spaces, Lecture Notes Math. 1477, Springer, Berlin, 1991. Zbl0743.46069
- [12] R. Jajte, Asymptotic formula for normal operators in non-commutative -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. Zbl0379.46060
- [14] E. C. Lance, Ergodic theorem for convex sets and operator algebras, ibid. 37 (1976), 201-214. Zbl0338.46054
- [15] D. Menchoff [D. Men'shov], Sur les séries de fonctions orthogonales, Fund. Math. 4 (1923), 82-105. Zbl49.0293.01
- [16] W. Orlicz, Zur Theorie der Orthogonalreihen, Bull. Internat. Acad. Polon. Sci. Sér. A 1927, 81-115. Zbl53.0265.05
- [17] A. Paszkiewicz, Convergence in W*-algebras, J. Funct. Anal. 69 (1986), 143-154. Zbl0612.46060
- [18] A. Paszkiewicz, A limit in probability in a W*-algebra is unique, ibid. 90 (1990), 429-444. Zbl0821.46081
- [19] D. Petz, Quasi-uniform ergodic theorems in von Neumann algebras, Bull. London Math. Soc. 16 (1984), 151-156. Zbl0535.46042
- [20] H. Rademacher, Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen, Math. Ann. 87 (1922), 112-138. Zbl48.0485.05
- [21] I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. 57 (1953), 401-457. Zbl0051.34201
- [22] Y. G. Sinai and V. V. Anshelevich, Some problems of non-commutative ergodic theory, Russian Math. Surveys 31 (1976), 157-174. Zbl0365.46053