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arXiv · 2302.05676

Uniform Banach-Saks properties

G. Grelier
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Abstract

The principal aim of this paper is to study the Banach-Saks property when the speed of convergence of a Cesaro mean sequence can be chosen independtly from the choice of the initial sequence. We establish links between the uniform Banach-Saks property, properties $(A_\infty)$ of Partington and the $p$-Banach-Saks property. We also prove that the $p$-Banach-Saks property and the strong $p$-Banach-Saks property are equivalent. Many examples are given and we apply the results to the symmetric Kottman constant.

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G. Grelier. 2023-02-11. Uniform Banach-Saks properties. https://arxiv.org/abs/2302.05676

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