Quantification of the Banach-Saks property

Autor:	Hana Bendová, Ondřej F. K. Kalenda, Jiří Spurný
Jazyk:	angličtina
Rok vydání:	2014
Předmět:	Discrete mathematics Unit sphere Mathematics - Functional Analysis Mathematics::Functional Analysis 46B20 Compact space Weak convergence Norm (mathematics) FOS: Mathematics Computer Science::Computational Complexity Analysis Functional Analysis (math.FA) Mathematics
Popis:	We investigate possible quantifications of the Banach-Saks property and the weak Banach-Saks property. We prove quantitative versions of relationships of the Banach-Saks property of a set with norm compactness and weak compactness. We further establish a quantitative version of the characterization of the weak Banach-Saks property of a set using uniform weak convergence and $\ell_1$-spreading models. We also study the case of the unit ball and in this case we prove a dichotomy which is an analogue of the James distortion theorem for $\ell_1$-spreading models. 18 pages; we added some references to related results, remarks on this relationship, the proof of one lemma was simplified
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::44fc0b63ae038d0d6ec20c6657ee333c http://arxiv.org/abs/1406.0684 Zobrazit plný text záznamu