Realizing irreducible semigroups and real algebras of compact operators |
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Authors: | Janez Bernik Mitja Mastnak |
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Institution: | a Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia b Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada |
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Abstract: | Let B(X) be the algebra of bounded operators on a complex Banach space X. Viewing B(X) as an algebra over 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? |
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Keywords: | Semigroup of operators Real algebra of operators Real spectrum Real trace Real form Weak real form Irreducibility |
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