Characterizations of the trace
type: Item
instance of: scholarly article
title: Characterizations of the trace
zbMATH Open document ID: 0661.15017
DOI: 10.1016/0024-3795(88)90050-X
author: Jaroslav Zemánek
author: Dénes Petz
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Extending a result of \textit{L. T. Gardner} [Can. J. Math. 31, 1322-1328 (1979; Zbl 0394.47059)] the authors prove the following: a linear functional on M(n,\({\mathbb{C}})\) is a (nonnegative) scalar multiple of the trace iff \(f(A^ k)=f(| A|^ k)\) for all \(A\in M(n,{\mathbb{C}})\) and some fixed k. Similar characterizations for more general operator algebras, in particular in terms of projections, are obtained.
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 4079636
zbMATH Keywords: linear functional
zbMATH Keywords: trace
zbMATH Keywords: operator algebras
zbMATH Keywords: projections
reviewed by: Vlastimil Pták
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4079636