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

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

2007-03-10

arxiv.org/abs/math/0703282v1

Mathematics

Operator Algebras

34 pages

Scientific paper

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.

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