A characterization of strongly weakly compactly generated Banach space
type: Item
instance of: scholarly article
title: A characterization of strongly weakly compactly generated Banach space
zbMATH Open document ID: 1067.46024
author: Dave Sobecki
published in: Rocky Mountain Journal of Mathematics
publication date: 2005-03-10T00:00:00Z
review text: A Banach space \(X\) is called strongly WCG if \(X\) contains a weakly compact subset \(K\) which almost absorbs any other weakly compact subset \(L\), i.e., for every \(\varepsilon>0\) there is \(n\) so that \(L\subset nK+\varepsilon B_X\). The author proves that for a strongly WCG space \(X\) there exists a reflexive space \(R\) and a continuous linear operator \(T:R\to X\) such that \(T(B_R)\) almost absorbs every weakly compact set. This result is analogous to the well-known Davis--Figiel--Johnson--Pełczyński factorization theorem and the proof is similar.
reviewed by: A. M. Plichko
Mathematics Subject Classification ID: 46B26
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 2143239
zbMATH Keywords: strongly WCG Banach space
zbMATH Keywords: Davis--Figiel--Johnson--Pełczyński factorisation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069812
OpenAlex ID: W2012194809
cites work: Factoring weakly compact operators
cites work: Q3254057
cites work: On strongly WCG Banach spaces
cites work: Q3995204
DOI: 10.1216/RMJM/1181069812
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description: scientific article; zbMATH DE number 2143239