The Mean Ergodic Theorem in symmetric spaces
Fedor SukochevSchool of Mathematics and Statistics University of New South Wales Kensington, 2052, NSW, AustraliaAleksandr VekslerV. I. Romanovskiy Institute of Mathematics Uzbekistan Academy of Sciences Tashkent, Uzbekistan
ABI
Abstract
We investigate the validity of the Mean Ergodic Theorem in a symmetric Banach function space $E$ associated to an atomless Lebesgue probability space $(\Omega , \nu )$. We show that the Mean Ergodic Theorem holds if and only if $E$ is separable. That is,
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