C*-bundles and C0(X)-algebras

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Abstract

We prove that a C0(X)-algebra is the section algebra of an upper semi-continuous C*-bundle over X. From this we obtain four corollaries. A C*-algebra A is the section algebra of an upper semi-continuous C*-bundle over Prim ZM(A). If X is a locally compact Hausdorff space and α:Prim A → X is a continuous map with dense range, then A is isomorphic to the section algebra of an upper semi-continuous C*-bundle over X. The induced algebra of an upper semi-continuous C*-bundle is an upper semi-continuous C*-bundle of induced algebras, when the action satisfies suitable condition. We give a necessary and sufficient condition for these bundles to be continuous. With a suitable twisted action, the twisted crossed product of an upper semi-continuous C*-bundle is an upper semi-continuous C*-bundle of twisted crossed products and the twisted crossed product of a continuous C*-bundle by an amenable group is again a continuous C*-bundle.

Original languageEnglish (US)
Pages (from-to)463-477
Number of pages15
JournalIndiana University Mathematics Journal
Volume45
Issue number2
StatePublished - Jun 1 1996
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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