Publication at Faculty of Mathematics and Physics |
2023
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 ξ-Banach-Saks sets using ξ+11-spreading models and a quantitative version of the relation of ξ-Banach-Saks sets, weak ξ-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.