Quantifying properties (K) and (µs)

0570593 - MÚ 2024 RIV DE eng J - Journal Article
Chen, D. - Kania, Tomasz - Ruan, Y.
Quantifying properties (K) and (µs).
Mathematische Nachrichten. Roč. 296, č. 3 (2023), s. 996-1012. ISSN 0025-584X. E-ISSN 1522-2616
Institutional support: RVO:67985840
Keywords : Banach-Saks property * Grothendieck property * property (K) * property (µs)
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1002/mana.202100198

A Banach space X has property (K), whenever every weak* null sequence in the dual space admits a convex block subsequence (Formula presented.) so that (Formula presented.) as (Formula presented.) for every weakly null sequence (Formula presented.) in X, X has property (Formula presented.) if every weak* null sequence in (Formula presented.) admits a subsequence so that all of its subsequences are Cesàro convergent to 0 with respect to the Mackey topology. Both property (Formula presented.) and reflexivity (or even the Grothendieck property) imply property (K). In this paper, we propose natural ways for quantifying the aforementioned properties in the spirit of recent results concerning other familiar properties of Banach spaces.
Permanent Link: https://hdl.handle.net/11104/0341894