Computing the norms of elementary operators
type: Item
instance of: scholarly article
title: Computing the norms of elementary operators
zbMATH Open document ID: 1053.47032
author: Richard M. Timoney
published in: Illinois Journal of Mathematics
publication date: 2004-01-19T00:00:00Z
review text: Let \(A\) be a \(C^*\)-algebra. Given an elementary operator \(T:A\rightarrow A\), \(Tx=\sum_{i=1}^la_ixb_i\), \(a_i,b_i\in M(A)\), \(i=1,\ldots,l\), the Haagerup estimate of the completely bounded norm \(\| T\| _{CB}\) is \[ \| T\| \leq\| T\| _{CB}\leq\sqrt{\left\| \sum_{j=1}^la_ja_j^*\right\| \,\left\| \sum_{j=1}^lb_j^*b_j\right\| }. \] The author characterizes equality in this inequality. The characterization is given in terms of extremal matrix numerical ranges, and for selfadjoint \(T\) an explicit \(k\) is given so that \(\| T\| _k=\| T\| _{CB}\). The \(C^*\)-algebras for which the equality is realized are characterized.
reviewed by: Martín Argerami
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 47L25
Mathematics Subject Classification ID: 47A12
zbMATH DE Number: 2028868
zbMATH Keywords: elementary operators
zbMATH Keywords: Haagerup estimate
zbMATH Keywords: completely bounded norm
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028868