Symétries isométriques, applications à la dualité des espaces réticulés
type: Item
instance of: scholarly article
title: Symétries isométriques, applications à la dualité des espaces réticulés
zbMATH Open document ID: 0537.46031
DOI: 10.1007/BF02763172
author: Gilles Godefroy
published in: Israel Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: As given in his abstract, the author proves the following results. (i) If E is a non-reflexive Banach lattice, there exists for every n a dual of finite even order of E which contains isometrically \(\ell^ 1_ n.\) (ii) The analogous result for \(\ell_ n^{\infty}\) when E is not weakly sequentially compact. (iii) If E is a Banach lattice which is isometric to the dual of a Banach space X, then the order interval is \(\sigma\) (E,X)-compact. (iv) Under various conditions, a Banach lattice which is a dual as a Banach space, is a dual as a Banach lattice. For terminology, see [\textit{H. H. Schaefer}, Banach lattices and positive operators, (1974; Zbl 0296.47023)].
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 3853779
zbMATH Keywords: duality
zbMATH Keywords: non-reflexive Banach lattice
zbMATH Keywords: order interval
reviewed by: Peng-Yee Lee
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02763172
OpenAlex ID: W1969450105
description: scientific article; zbMATH DE number 3853779