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36th Canadian Operator Symposium(COSy)
May 20-24, 2008
The Fields Institute
University of Toronto, Ontario, Canada

Organizers
Man-Duen Choi, George Elliott, Raphael Ponge, Andrew Toms

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Realizing irreducuble semigroups and real algebras of compact operators
by
Mitja Mastnak
University of Waterloo
Coauthors: J Bernik, H. Radjavi

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?

Date received: April 11, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawx-09.