On certain classes of Markushevich bases
type: Item
instance of: scholarly article
title: On certain classes of Markushevich bases
zbMATH Open document ID: 0808.46010
DOI: 10.1007/BF01196436
published in: Archiv der Mathematik
publication date: 1994-06-15T00:00:00Z
review text: It is shown in this paper that if \(X\) is a Banach space for which \(X^*\) has a Markushevich basis \((u_ i,z_ i)\) with \([z_ i]\) containing \(X\) and \(B(X^*)\) is of countable tightness in the \(\omega^*\)-topology (see the paper for the technical definition), then \(X\) is weakly compactly generated. Other results (having similarly technical assumptions) which imply the non-existence of certain types of Markushevich bases are also derived.
reviewed by: James R. Holub
Mathematics Subject Classification ID: 46A35
zbMATH DE Number: 590075
zbMATH Keywords: Markushevich basis
zbMATH Keywords: countable tightness
zbMATH Keywords: \(\omega^*\)-topology
zbMATH Keywords: weakly compactly generated
author: Manuel Valdivia
MaRDI profile type: Publication
cites work: Function spaces in the topology of pointwise convergence, and compact sets
cites work: Problèmes de renormages. (Renorming problems)
cites work: Q3134552
cites work: A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space
cites work: Some remarks on weakly compactly generated Banach spaces
cites work: Q4136031
cites work: On a theorem of Sobczyk
cites work: A function space C(X) which is weakly Lindelöf but not weakly compactly generated
cites work: Q5631608
cites work: Q3920145
cites work: Simultaneous resolutions of the identity operator in normed spaces
cites work: On one generalization of weakly compactly generated Banach spaces
cites work: Countable Paracompactness, Normality, and Moore Spaces.
description: scientific article; zbMATH DE number 590075