Stochastic Banach principle in operator algebras

被引：1
|
作者：
Grabarnik, Genady Ya.
Shwartz, Laura
机构：
[1] IBM TJ Watson Res Ctr, Hawthorne, NY 10532 USA
[2] Univ S Africa, Dept Math, ZA-0003 Pretoria, South Africa
来源：
STUDIA MATHEMATICA | 2007年 / 180卷 / 03期
关键词：
Banach principle; von Neumann algebras; non-commutative ergodic theorems; stochastic convergence;
D O I：
10.4064/sm180-3-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The classical Banach principle is an essential tool for the investigation of ergodic properties of Cesaro subsequences. The aim of this work is to extend the Banach principle to the case of stochastic convergence in operator algebras. We start by establishing a sufficient condition for stochastic convergence (stochastic Banach principle). Then we prove stochastic convergence for bounded Besicovitch sequences, and as a consequence for uniform subsequences.
引用
收藏
页码：255 / 270
页数：16
相关论文
共 50 条
  • [1] Are operator algebras Banach algebras?
    Blecher, DP
    [J]. BANACH ALGEBRAS AND THEIR APPLICATIONS, 2004, 363 : 53 - 58
  • [2] Duality and operator algebras II: operator algebras as Banach algebras
    Blecher, DP
    Magajna, B
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 226 (02) : 485 - 493
  • [3] Roots in Operator and Banach Algebras
    David P. Blecher
    Zhenhua Wang
    [J]. Integral Equations and Operator Theory, 2016, 85 : 63 - 90
  • [4] Roots in Operator and Banach Algebras
    Blecher, David P.
    Wang, Zhenhua
    [J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2016, 85 (01) : 63 - 90
  • [5] BANACH ALGEBRAS OF OPERATOR SEQUENCES
    Seidel, M.
    Silbermann, B.
    [J]. OPERATORS AND MATRICES, 2012, 6 (03): : 385 - 432
  • [6] Linearity of Maps on Banach and Operator Algebras
    Turilova, E.
    Hamhalter, J.
    [J]. LOBACHEVSKII JOURNAL OF MATHEMATICS, 2020, 41 (03) : 435 - 439
  • [7] On the simplicial cohomology of Banach operator algebras
    Blanco, A.
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 261 (01) : 111 - 148
  • [8] Linearity of Maps on Banach and Operator Algebras
    E. Turilova
    J. Hamhalter
    [J]. Lobachevskii Journal of Mathematics, 2020, 41 : 435 - 439
  • [9] Hyperreflexivity of Operator Algebras of the Banach Space
    YUAN Guo-chang
    [J]. Chinese Quarterly Journal of Mathematics, 2005, (02) : 178 - 184
  • [10] REFLEXIVE OPERATOR ALGEBRAS ON BANACH SPACES
    Merlevede, Florence
    Peligrad, Costel
    Peligrad, Magda
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2014, 267 (02) : 451 - 464
12345