Discrete product systems of Hilbert bimodules

Details Discrete product systems of Hilbert bimodules Discrete product systems of Hilbert bimodules

1999-04-21

arxiv.org/abs/math/9904115v1

Mathematics

Operator Algebras

38 pages, AMS-LaTeX

Scientific paper

A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together with a left action of A as adjointable operators on X. We consider families X = {X_s :s\in P} of Hilbert bimodules, indexed by a semigroup P, which are endowed with a multiplication which implements isomorphisms X_s\otimes_A X_t \to X_{st}; such a family is a called a product system. We define a generalized Cuntz- Pimsner algebra O_X, and we show that every twisted crossed product of A by P can be realized as O_X for a suitable product system X. Assuming P is quasi- lattice ordered in the sense of Nica, we analyze a certain Toeplitz extension T_{cov}(X) of O_X by embedding it in a crossed product B_P \times_{\tau,X} P which has been ``twisted'' by X; our main Theorem is a characterization of the faithful representations of B_P \times_{\tau,X} P.

Affiliated with

Also associated with

No associations

Rating

Discrete product systems of Hilbert bimodules 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 Discrete product systems of Hilbert bimodules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete product systems of Hilbert bimodules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-70727