Atlas: Morita-Rieffel Equivalence and Spectral Theory for Integrable Automorphism Groups of C*-Algebras by Ruy Exel

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18th International Conference on Operator Theory
June 27 - July 1, 2000
University of the West
Timisoara, Romania

Organizers
Dumitru Gaspar, Traian Ceausu, Aurelian Craciunescu, Aurelian Gheondea, Radu-Nicolae Gologan, Ciprian Pop, Dan Popovici, Nicolae Suciu, Alexandru Terescenco, Dan Timotin, Flavius Turcu

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Morita-Rieffel Equivalence and Spectral Theory for Integrable Automorphism Groups of C*-Algebras
by
Ruy Exel
Universidade Federal de Santa Catarina - Florianopolis

Given a C*-dynamical system (A, G, \alpha), we discuss conditions under which subalgebras of the multiplier algebra M(A) consisting of fixed points for \alpha are Morita-Rieffel equivalent to ideals in the crossed product of A by G. In case G is abelian we also develop a spectral theory, giving a necessary and sufficient condition for \alpha to be equivalent to the dual action on the cross-sectional C*-algebra of a Fell bundle. In our main application we show that a proper action of an abelian group on a locally compact space is equivalent to a dual action.

http://www.mtm.ufsc.br/~exel/FILES/spec.tex

Date received: May 23, 2000