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

Ruy Exel

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arXiv · math/9904094

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

Ruy Exel

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Abstract

Given a C*-dynamical system (A,G,α), we discuss conditions under which subalgebras of the multiplier algebra M(A) consisting of fixed points for αare 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 αto 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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BibTeX RIS

Ruy Exel. 1999-04-19. Morita-Rieffel Equivalence and Spectral Theory for Integrable Automorphism Groups of C*-Algebras. https://arxiv.org/abs/math/9904094

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