Ergodic theorems in symmetric sequence spaces
Volume 156 / 2019
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 $E \not =l_1$.
