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arXiv · 2111.12773

Quantification of Banach-Saks properties of higher orders

Zdeněk Silber
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Abstract

We investigate possible quantifications of Banach-Saks sets and weak Banach-Saks sets of higher orders and their relations to other quantities. We prove a quantitative version of the characterization of weak $\xi$-Banach-Saks sets using $\ell_1^{\xi+1}$-spreading models and a quantitative version of the relation of $\xi$-Banach-Saks sets, weak $\xi$-Banach-Saks sets, norm compactness and weak compactness. We further introduce a new measure of weak compactness. Finally, we provide some examples showing the limitations of these quantifications.

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BibTeXRIS

Zdeněk Silber. 2021-11-24. Quantification of Banach-Saks properties of higher orders. https://doi.org/10.1016/j.jmaa.2022.126590

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