Continuous spectral decompositions of Abelian group actions on C*-algebras

Abstract

Let G be a locally compact Abelian group. Following Ruy Exel, we view Fell bundles over the Pontrjagin dual of G as continuous spectral decompositions of G-actions on C*-algebras. We classify such spectral decompositions using certain dense subspaces related to Marc Rieffel's theory of square-integrability. There is a unique continuous spectral decomposition if the group acts properly on the primitive ideal space of the C*-algebra. But there are also examples of group actions without or with several inequivalent spectral decompositions.

34 pages

References in corpus (2)

• Equivariant Kasparov theory and generalized homomorphisms
• Generalized fixed point algebras and square-integrable group actions

Cited by in corpus (5)

• A generalized Fourier inversion theorem
• Integrability of dual coactions on Fell bundle C*-algebras
• Generalized fixed point algebras for coactions of locally compact quantum groups
• Rieffel proper actions
• Crossed module actions on continuous trace $C^{\ast }$-algebras