✦ LIBER ✦
Morita–Rieffel Equivalence and Spectral Theory for Integrable Automorphism Groups of C*-Algebras
✍ Scribed by Ruy Exel
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 360 KB
- Volume
- 172
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
Given a C*-dynamical system (A, G, :), we discuss conditions under which subalgebras of the multiplier algebra M(A) consisting of fixed points for : 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 : 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.