Dual action of asymptotically isometric copies of \(\ell_p\) \((1 \leq p < \infty)\) and \(c_0\)
type: Item
instance of: scholarly article
title: Dual action of asymptotically isometric copies of \(\ell_p\) \((1 \leq p < \infty)\) and \(c_0\)
zbMATH Open document ID: 0892.46014
author: S. Chen
author: Bor-Luh Lin
published in: Collectanea Mathematica
publication date: 1997-09-15T00:00:00Z
full work available at URL: https://eudml.org/doc/40707
review text: P. N. Dowling and C. J. Lennard proved that if a Banach space contains an asymptotically isometric copy of \(\ell_1\), then it fails the fixed point property. In this paper, necessary and sufficient conditions for a Banach space to contain an asymptotically isometric copy of \(\ell_p\) \((1\leq p<\infty)\) or \(c_0\) are given by the dual action. In particular, it is shown that a Banach space contains an asymptotically isometric copy of \(\ell_1\) if its dual space contains an isometric copy of \(\ell_\infty\), and if a Banach space contains an asymptotically isometric copy of \(c_0\), then its dual space contains an asymptotically isometric copy of \(\ell_1\).
Mathematics Subject Classification ID: 46B45
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 1060656
zbMATH Keywords: asymptotically isometric copy
zbMATH Keywords: fixed point property
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1060656