Ergodicity and super weak compactness
Functional Analysis
2023-02-14 v1
Abstract
We prove that a closed convex subset of a Banach space is (super-)weakly compact if and only if it is (super)-ergodic. As a consequence we deduce that super weakly compact sets are characterized by the fixed point property for continuous affine mappings. We also prove that the M-(fixed point property for affine isometries) implies the Banach-Saks property.
Cite
@article{arxiv.2302.05656,
title = {Ergodicity and super weak compactness},
author = {Guillaume Grelier and Matías Raja},
journal= {arXiv preprint arXiv:2302.05656},
year = {2023}
}