Realizing irreducible semigroups and real algebras of compact operators
type: Item
instance of: scholarly article
title: Realizing irreducible semigroups and real algebras of compact operators
zbMATH Open document ID: 1153.47026
author: J. Bernik
author: Mitja Mastnak
author: H. Radjavi
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-10-22T00:00:00Z
review text: From the abstract: Let \({\mathcal B}(X)\) be the algebra of bounded operators on a complex Banach space \(X\). Viewing \({\mathcal B}(X)\) as an algebra over \(\mathbb R\), we study the structure of those irreducible subalgebras which contain nonzero compact operators. In particular, irreducible algebras of trace-class operators with real trace are characterized. This yields an extension of Brauer-type results on matrices to operators in infinite dimensions, answering the question: is an irreducible semigroup of compact operators with real spectra realizable, i.e., simultaneously similar to a semigroup whose matrices are real?
reviewed by: Nguyen Van Minh
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47A99
zbMATH DE Number: 5355967
zbMATH Keywords: semigroup of operators
zbMATH Keywords: real algebra of operators
zbMATH Keywords: real spectrum
zbMATH Keywords: real trace
zbMATH Keywords: real form
zbMATH Keywords: weak real form
zbMATH Keywords: irreducibility
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.08.002
OpenAlex ID: W1968286996
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DOI: 10.1016/J.JMAA.2008.08.002
description: scientific article; zbMATH DE number 5355967