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).
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页码：949 / 966
页数：18
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