Joint similarity problems and the generation of operator algebras with bounded length
type: Item
instance of: scholarly article
title: Joint similarity problems and the generation of operator algebras with bounded length
zbMATH Open document ID: 0932.47015
DOI: 10.1007/BF01195125
author: Gilles Pisier
published in: Integral Equations and Operator Theory
publication date: 2000-03-07T00:00:00Z
review text: The author obtains an example of a pair of commuting Hilbert space operators \((T_1,T_2)\) such that each of them is similar to a contraction but the pair \((T_1,T_2)\) is not similar to a pair of contractions. The same ideas allows to obtain a pair of commuting unitarizable representations \((\pi_1,\pi_2)\) on the free group with \(N\geq 2\) generators such that \((\pi_1,\pi_2)\) is not similar to a pair of unitary representations. In connection with these examples the author introduces a notion of a length for an operator algebra generated by two subalgebras and studies the length of the maximal tensor product of two \(C^\ast\)-algebras.
Mathematics Subject Classification ID: 47A65
Mathematics Subject Classification ID: 46L06
Mathematics Subject Classification ID: 46M05
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1203951
zbMATH Keywords: contraction
zbMATH Keywords: unitarizable representation
zbMATH Keywords: length of an operator algebra
zbMATH Keywords: maximal tensor product of two \(C^*\)-algebras
reviewed by: Andrzej Sołtysiak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1203951