On a result of Peetre about interpolation of operator spaces
type: Item
instance of: scholarly article
title: On a result of Peetre about interpolation of operator spaces
zbMATH Open document ID: 0979.46013
DOI: 10.5565/PUBLMAT_44200_06
author: Fernando Cobos
author: Teresa Signes
published in: Publicacions Matemàtiques
publication date: 2001-10-24T00:00:00Z
full work available at URL: https://eudml.org/doc/41400
review text: For quasi-normed operator ideals \({\mathcal J}\), the authors find conditions on couples of Banach spaces (such as regularity, quasi-linearizability), or on \({\mathcal J}\) (such as injectivity or surjectivity), and on the interpolation parameters, that allow to establish inclusion relations between \({\mathcal J}(A,B)\) and real interpolated spaces of couples \(({\mathcal J}(A,B_0),{\mathcal J}(A,B_1))\) or \(({\mathcal J}(A_0,B),{\mathcal J}(A_1,B))\)), when \(B\) is an intermediate space with respect to \((B_0,B_1)\) or \(A\) is an intermediate space with respect to \((A_0,A_1)\), respectively. They apply their results to identify some interpolated spaces between couples of spaces of operators and of tensor products, in the direction of previous results due to Kouba and to Ovchinnikov.
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 47L20
Mathematics Subject Classification ID: 46M35
zbMATH DE Number: 1563893
zbMATH Keywords: real interpolation
zbMATH Keywords: quasi-normed operator ideals
zbMATH Keywords: tensor product
zbMATH Keywords: regularity
zbMATH Keywords: linearizability
zbMATH Keywords: injectivity
zbMATH Keywords: surjectivity
zbMATH Keywords: inclusion relations
reviewed by: Joan Cerdà
MaRDI profile type: Publication
OpenAlex ID: W2119106660
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description: scientific article; zbMATH DE number 1563893