Ergodic theorems in symmetric sequence spaces
Vladimir ChilinNational University of Uzbekistan 700174 Tashkent, UzbekistanAzizkhon AzizovNational University of Uzbekistan 700174 Tashkent, Uzbekistan
ABI
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 $E \not =l_1$.
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