Köthe spaces with preequivalent unconditional bases
type: Item
instance of: scholarly article
title: Köthe spaces with preequivalent unconditional bases
zbMATH Open document ID: 1027.46007
author: M. M. Dragilev
published in: Russian Mathematics
publication date: 2002-06-09T00:00:00Z
review text: Let \(X\) be a metrizable Köthe space and let \(X'\) be the conjugate space of \(X\). The author proves that (1) in \(X\), all of its unconditional bases are pre-equivalent if and only if \(X\) is isomorphic to one of the spaces \(\ell_1\), \(\ell_2\), \(c_0\) and \(\omega\) (Theorem 1), and (2) in \(X'= \{X',\sigma^*(X', X))\), all of its unconditional Schauder bases are pre-equivalent if and only if \(X'\) is isomorphic to one of the spaces \(\varphi\), \((\ell_1,\sigma^*(\ell_1,c_0))\), \((\ell_2,\sigma^*(\ell_2,\ell_2))\), \((\ell_\infty, \sigma^*(\ell_\infty, \ell_1))\), where \(\sigma^*\) stands for normal topology (Corollary 2). Note that two bases in a topological vector space are said to be pre-equivalent if they can be reduced to the coincidence by a linear automorphism of the space and the norming of elements.
reviewed by: Toivo Leiger
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46B45
Mathematics Subject Classification ID: 46A35
zbMATH DE Number: 1752712
zbMATH Keywords: Köthe space
zbMATH Keywords: unconditional basis
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1752712