Discovering the algebraic structure on the metric injective envelope of a real Banach space
type: Item
instance of: scholarly article
title: Discovering the algebraic structure on the metric injective envelope of a real Banach space
zbMATH Open document ID: 0912.46072
DOI: 10.1016/S0166-8641(96)00157-5
published in: Topology and its Applications
publication date: 1999-05-26T00:00:00Z
review text: By \textit{H. B. Cohen} [Bull. Am. Math. Soc. 70, 723-726 (1964; Zbl 0124.06505)], every real Banach space \(X\) admits an injective envelope, i.e. there exists a real injective Banach space \(\varepsilon\ell X\) and a linear isometry \(e: X\to \varepsilon\ell X\) such that the smallest injective subspace of \(\varepsilon\ell X\) containing \(e(X)\) is \(\varepsilon\ell X\) itself. In the present paper, the authors give an alternative construction of an injective envelope by introducing the structure of a Banach space on the injective metric envelope \(\varepsilon mX\) of \(X\), defined by Isbell. In doing this, they answer a question of \textit{J. R. Isbell} [J. Math. Anal. Appl. 27, 516-518 (1969; Zbl 0206.42201)].
reviewed by: Reinhold Meise
Mathematics Subject Classification ID: 46M10
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 46B99
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 1038789
zbMATH Keywords: linear injective envelope
zbMATH Keywords: real injective Banach space
zbMATH Keywords: injective metric envelope
author: Filomena Cianciaruso
author: E. De Pascale
MaRDI profile type: Publication
Wikidata QID: Q114121889
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description: scientific article; zbMATH DE number 1038789