On interpolation of Banach algebras and factorization of weakly compact homomorphisms
type: Item
instance of: scholarly article
title: On interpolation of Banach algebras and factorization of weakly compact homomorphisms
zbMATH Open document ID: 1119.46024
author: Fernando Cobos
author: Luz M. Fernández-Cabrera
author: Antón Martínez
published in: Bulletin des Sciences Mathématiques
publication date: 2007-02-20T00:00:00Z
review text: The family \((\cdot,\cdot)_\Gamma\) of interpolation methods was introduced by \textit{J.\,Peetre} [``A theory of interpolation of normed spaces'' (Notas Mat.\ No.\ 39) (1968; Zbl 0162.44502)]. A special class of the family \(\Gamma\) was used in [\textit{A.\,Blanco, S.\,Kaijser} and \textit{T.\,J.\thinspace Ransford}, J.~Funct.\ Anal.\ 217, No.\,1, 126--141 (2004; Zbl 1078.46050)] to prove that weakly compact homomorphisms between Banach algebras factor through a reflexive Banach algebra. It is crucial in this factorization that the interpolation method preserves the Banach algebra structure. In the paper under review, a necessary and sufficient condition on \(\Gamma\) for the interpolation method \((\cdot,\cdot)_\Gamma\) to preserve the Banach algebra structure is found. Applying this general result, it turns out that the classical real interpolation method \((\cdot,\cdot)_{\theta,q}\) preserves Banach algebras only if \(q=1\). Also, some results on the factorization of weakly compact homomorphisms between Banach algebras are derived as applications.
reviewed by: Olav Nygaard
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 46M35
zbMATH DE Number: 5128466
zbMATH Keywords: Real interpolation
zbMATH Keywords: Banach algebra
zbMATH Keywords: Factoring weakly compact homomorphisms
MaRDI profile type: Publication
full work available at URL: j.bulsci.2005.12.003
OpenAlex ID: W1989414582
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DOI: 10.1016/J.BULSCI.2005.12.003
description: scientific article; zbMATH DE number 5128466