Uniqueness of the unconditional basis of \(\ell_{1}(\ell_p)\) and \(\ell_p(\ell_1)\), \(0<p<1\)
type: Item
instance of: scholarly article
title: Uniqueness of the unconditional basis of \(\ell_{1}(\ell_p)\) and \(\ell_p(\ell_1)\), \(0<p<1\)
zbMATH Open document ID: 1084.46002
author: N. J. Kalton
author: F. Albiac
author: C. Leránoz
published in: Positivity
publication date: 2005-06-13T00:00:00Z
review text: It was shown by \textit{C. Leránoz} [Stud. Math. 102, 193--207 (1992; Zbl 0812.46003)] that the spaces \(c_0(\ell_p)\) \((0<p<1)\) have a unique normalized unconditional basis up to permutation and, later on, the authors proved in [Stud. Math. 150, 35--52 (2002; Zbl 1031.46006)] the uniqueness of an unconditional basis up to permutation of \(\ell_p(c_0)\) and \(\ell_p(\ell_2)\) for \(0<p<1\). Here the same result is proved for the quasi-Banach spaces \(\ell_1(\ell_p)\) and \(\ell_p(\ell_1)\) \((0<p<1)\): they have a unique unconditional basis up to a permutation.
Mathematics Subject Classification ID: 46A16
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 46B45
zbMATH DE Number: 2175439
zbMATH Keywords: uniqueness
zbMATH Keywords: unconditional basis
zbMATH Keywords: quasi-Banach space
MaRDI profile type: Publication
full work available at URL: s11117-003-8542-z
OpenAlex ID: W2030018146
cites work: Uniqueness of unconditional basis of \(\ell_{p}(c_{0})\) and \(\ell_{p}(\ell_{2})\), \(0<p<1\)
cites work: Banach spaces with a unique unconditional basis, up to permutation
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cites work: Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces
cites work: Banach spaces with a unique unconditional basis
cites work: Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces. II
DOI: 10.1007/S11117-003-8542-Z
description: scientific article; zbMATH DE number 2175439