C*-algebras of Hilbert module product systems

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12 Scopus citations


We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are K-contractible. One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product by ℝ considered by Rieffel and by Pimsner and Voiculescu, and can be used to produce a new proof of Connes' analogue of the Thom isomorphism and in particular of Bott periodicity. Another special case is closely related to Arveson's spectral C*-algebras, and is used to settle Arveson's problem of computing their K-theory, extending earlier results of Zacharias to cover the general case.

Original languageEnglish
Pages (from-to)131-142
Number of pages12
JournalJournal fur die Reine und Angewandte Mathematik
Issue number570
StatePublished - 1 Jan 2004
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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