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## Studia Mathematica

2000 | 143 | 1 | 33-41
Tytuł artykułu

### Banach principle in the space of τ-measurable operators

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
33-41
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-06-20
poprawiono
2000-06-21
Twórcy
autor
• Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
autor
• Department of Mathematics, North Dakota State University, Fargo, ND 58105, U.S.A.
Bibliografia
• [BJ] A. Bellow and R. L. Jones, A Banach Principle for $L^∞$, Adv. Math. 120 (1996), 115-172.
• [BR] O. Bratteli and D. N. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer, Berlin, 1979.
• [DS] N. Dunford and J. T. Schwartz, Linear Operators I, Wiley, New York, 1958.
• [FK] T. Fack and H. Kosaki, Generalized s-numbers of τ-mesurable operators, Pacific J. Math. 123 (1986), 269-300.
• [Ga] A. Garsia, Topics in Almost Everywhere Convergence, Lectures in Adv. Math. 4, Markham, Chicago, 1970.
• [Ja] R. Jajte, Strong Limit Theorems in Non-Commutative Probability, Lecture Notes in Math. 1110, Springer, Berlin, 1985.
• [La] E. C. Lance, Non-commutative ergodic theory, in: Proc. Meeting on C*-Algebras and Their Applications to Theoretical Physics, Roma, 1975, 70-79.
• [Li] S. Litvinov, On individual ergodic theorems with operator-valued Besicovitch's weights, to be submitted.
• [LM] S. Litvinov and F. Mukhamedov, On individual subsequential ergodic theorem in von Neumann algebras, Studia Math, to appear.
• [Ne] E. Nelson, Notes on non-commutative integration, J. Funct. Anal. 15 (1974), 103-116.
• [Pa] A. Paszkiewicz, Convergences in W*-algebras, ibid. 69 (1986), 143-154.
• [Se] I. Segal, A non-commutative extension of abstract integration, Ann. of Math. 57 (1953), 401-457.
• [Ta] M. Takesaki, Theory of Operator Algebras I, Springer, Berlin, 1979.
• [Ye] F. J. Yeadon, Ergodic theorems for semifinite von Neumann algebras I, J. London Math. Soc. (2) 16 (1977), 326-332.
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Bibliografia
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