Mean Ergodic Theorems in Symmetric Spaces of Measurable Functions

被引：0

作者：

Muratov, M. ^{[1
,2
]}

Pashkova, Yu ^{[1
,2
]}

Rubshtein, B-Z ^{[1
,2
]}

机构：

[1] VI Vernadsky Crimean Fed Univ, Simferopol 295007, Russia

[2] Ben Gurion Univ Negev, IL-84105 Beer Sheva, Israel

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2021年 / 42卷 / 05期

关键词：

symmetric spaces; ergodic theorems; Cesaro averages; absolute contractions; norm convergence; conservative and strictly conservative operators;

D O I：

10.1134/S1995080221050103

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E = E(Omega, F, mu) be a symmetric Banach space of measurable functions on a measure space (Omega, F, mu). We prove a version of Mean (Statistical) Ergodic Theorem for Cesaro averages A(n),(T) f = 1/n Sigma(n)(k=1) Tk-1 f, f is an element of E, while operators on E are induced by positive absolute contraction in L-1 + L-infinity = (L-1 + L-infinity)(Omega, F, mu).

引用

页码：949 / 966

页数：18

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