Ergodic theorems in symmetric sequence spaces

Vladimir Chilin; Azizkhon Azizov

doi:10.4064/cm7384-2-2018

Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

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Ergodic theorems in symmetric sequence spaces

Volume 156 / 2019

Vladimir Chilin, Azizkhon Azizov Colloquium Mathematicum 156 (2019), 57-68 MSC: 37A30, 46E30, 47A35. DOI: 10.4064/cm7384-2-2018 Published online: 14 December 2018

Abstract

It is proved that the averages $n^{-1} \sum _{k=0}^{n-1}T^k$ , where $T$ is a Dunford–Schwartz operator, strongly converge in a symmetric sequence space $E$ if and only if $E$ is separable and $E \not =l_1$ .

Authors

Vladimir ChilinNational University of Uzbekistan
700174 Tashkent, Uzbekistan
e-mail
Azizkhon AzizovNational University of Uzbekistan
700174 Tashkent, Uzbekistan
e-mail

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Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

Colloquium Mathematicum

Ergodic theorems in symmetric sequence spaces

Volume 156 / 2019

Abstract

Authors

Search for IMPAN publications

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