On the geometry of higher duals of a Banach space
type: Item
instance of: scholarly article
title: On the geometry of higher duals of a Banach space
zbMATH Open document ID: 1007.46016
author: T.S.S.R.K. Rao
published in: Illinois Journal of Mathematics
publication date: 2002-04-28T00:00:00Z
review text: A Banach space \(X\) is said to be an \(M\)-embedded space if the canonical image \(i_X(X)\) is an \(M\)-ideal in the bidual \(X^{**}\) [\textit{P. Harmand, D. Werner} and \textit{W. Werner}, ``\(M\)-ideals in Banach spaces and Banach algebras'', Lect. Notes Math. 1547, Berlin (1993; Zbl 0789.46011)]. It is shown that an \(M\)-embedded, non-reflexive space is an \(M\)-ideal, under the appropriate composition of the canonical embeddings, in all duals of even order. It is deduced that continuous linear functionals on such spaces have unique norm preserving extensions to all even order duals.
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 1734201
zbMATH Keywords: Banach space
zbMATH Keywords: higher duals
zbMATH Keywords: M-ideals
zbMATH Keywords: norm preserving extensions
reviewed by: Srinivasa Swaminathan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1734201