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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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