On \(c_ 0\) sequences in Banach spaces
type: Item
instance of: scholarly article
title: On \(c_ 0\) sequences in Banach spaces
zbMATH Open document ID: 0731.46007
DOI: 10.1007/BF02937292
published in: Israel Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: A Banach space has property (S) if every normalized weakly null sequence contains a subsequence equivalent to the canonical basis of \((c_ 0)\). It is shown that equivalence constants can be choosen independent of the original sequence. It is also shown that property (S) implies property (a) introduced by \textit{A. Pelczynski} [Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron Phys. 6, 251-253 (1958; Zbl 0082.108)]. This settles - in the negative - a conjecture by \textit{J. Hagler} [Stud. Math. 60, 289-307 (1977; Zbl 0387.46015)] that certain separable Banach spaces with property (a) have separable duals.
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46B03
zbMATH DE Number: 4208820
zbMATH Keywords: property (S)
zbMATH Keywords: property (a)
author: Helmut Knaust
author: E. Odell
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208820