Another version of Maher's inequality
type: Item
instance of: scholarly article
title: Another version of Maher's inequality
zbMATH Open document ID: 1085.47045
DOI: 10.4171/ZAA/1200
author: Salah Mecheri
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2004-11-01T00:00:00Z
review text: For a separable, infinite-dimensional Hilbert space \(H\), let \(L(H)\) denote the \(C^*\)-algebra of bounded linear operators on~\(H\). For two \(n\)-tuples of operators \(A=(A_1,\ldots,A_n)\), \(B=(B_1,\ldots,B_n)\) in \(L(H)\), let \(\Delta_{A,B}\) denote the following elementary operator on \(L(H)\): \[ X\mapsto\sum_{i=1}^nA_iXB_i-X. \] Fix \(T\in\ker\Delta_{A,B}\cap C_p\), where \(C_p\) is the \(p\)-th Schatten class and let \(F_p\) be defined by \[ F_p(X)=\| T-\Delta_{A,B}(X)\| _p^p. \] The author obtains several results on global minimizers and critical points for~\(F_p\). These results make essential use of the results by \textit{A.~Turnšek} in [Linear Algebra Appl. 317, 207--216 (2000; Zbl 1084.47510)].
reviewed by: Martin Mathieu
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 47B20
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 2112822
zbMATH Keywords: elementary operators
zbMATH Keywords: Maher's inequality
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2112822