Frames of multipliers in tensor products of Hilbert modules over pro-\(C^{*}\)-algebras
type: Item
instance of: scholarly article
title: Frames of multipliers in tensor products of Hilbert modules over pro-\(C^{*}\)-algebras
zbMATH Open document ID: 1195.46060
author: Maria Joiţa
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-05-10T00:00:00Z
review text: \textit{M.\,Frank} and \textit{D.\,Larson} [Contemp.\ Math.\ 247, 207--233 (1999; Zbl 0949.46027)] generalized the notion of frame to the setting of Hilbert \(C^*\)-modules. \textit{I.\,Raeburn} and \textit{S.\,J.\thinspace Thompson} [Proc.\ Am.\ Math.\ Soc.\ 131, No.\,5, 1557--1564 (2003; Zbl 1015.46034)] introduced the notion of standard frame of multipliers for a Hilbert \(C^*\)-module. In the paper under review, the author extends a result of \textit{A.\,Khosravi} and \textit{B.\,Khosravi} [Proc.\ Indian Acad.\ Sci., Math.\ Sci.\ 117, No.\,1, 1--12 (2007; Zbl 1125.46048)] for standard frames of multipliers. For a standard frame of multipliers for a Hilbert \(A\)-module \(E\) and a standard frame of multipliers for a Hilbert \(B\)-module \(F\), she constructs a standard frame of multipliers for the external tensor product of \(E\) and \(F\) and for the inner tensor product of \(E\) and \(F\), using a nondegenerate pro-\(C^*\)-morphism from \(A\) to the pro-\(C^*\)-algebra of all adjointable module morphisms on \(F\).
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 46L08
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46C05
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 5706223
zbMATH Keywords: Hilbert modules
zbMATH Keywords: standard frames
zbMATH Keywords: multipliers
zbMATH Keywords: pro-\(C^{*}\)-algebras
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.01.064
OpenAlex ID: W2119060841
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DOI: 10.1016/J.JMAA.2010.01.064
description: scientific article; zbMATH DE number 5706223