On automorphic Banach spaces
type: Item
instance of: scholarly article
title: On automorphic Banach spaces
zbMATH Open document ID: 1171.46048
author: Yolanda Moreno
author: A. M. Plichko
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: A Banach space \(X\) is called automorphic if, for every subspace \(E\) of \(X\), every into isomorphism \(T:E\to X\) extends to an automorphism of \(X\) (provided, of course, that \(X/E\) and \(X/T(E)\) have the same density character). Until now, only Hilbert spaces and \(c_0\) were known to be automorphic. This tour de force shows that \(c_0(\Gamma)\) is also automorphic when \(\Gamma\) is uncountable. A number of Banach spaces are proved not to be automorphic, including Gurariĭ's space, and at least one hereditarily indecomposable space.
Mathematics Subject Classification ID: 46M18
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 5508732
zbMATH Keywords: automorphism
zbMATH Keywords: Banach space
MaRDI profile type: Publication
full work available at URL: s11856-009-0002-4
OpenAlex ID: W2004686701
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DOI: 10.1007/S11856-009-0002-4
description: scientific article; zbMATH DE number 5508732