C*-algebras of Hilbert module product systems

Details C*-algebras of Hilbert module product systems C*-algebras of Hilbert module product systems

2002-05-23

arxiv.org/abs/math/0205238v2

Mathematics

Operator Algebras

11 pages (added an example and an appendix, corrected typos and improved exposition)

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

C*-algebras of Hilbert module product systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with C*-algebras of Hilbert module product systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and C*-algebras of Hilbert module product systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-454533