Morita-Rieffel Equivalence and Spectral Theory for Integrable Automorphism Groups of C*-Algebras

Details Morita-Rieffel Equivalence and Spectral Theory for Integrable Automorphism Groups of C*-Algebras Morita-Rieffel Equivalence and Spectral Theory for Integrable Automorphism Groups of C*-Algebras

1999-04-19

arxiv.org/abs/math/9904094v1

Mathematics

Operator Algebras

Plain TeX, 40 pages, no figures

Scientific paper

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.

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