Continuous tensor products and Arveson's spectral C*-algebras

We introduce a notion of continuous tensor products of Hilbert spaces which is closely related to Arveson's product systems and Araki and Woods' Boole an algebras of tensor decompositions. There is a classification into type I , II and III, and we can extend a result of Araki and Woods which classifie s the type I case as the symmetric Fock space over a direct integral of Hil bert spaces. There are also easy examples of type III. To any continuous te nsor product T we associate a nonsimple C*-algebra A(T) and show it to be s tably projectionless nuclear prime and infinite. It may be viewed as a cont inuous analogue of a UHE-algebra. In case of constant multiplicity n in the direct integral we obtain a sequence A(n) of C*-algebras which turn out to be KK-contractible. They carry an action of R such that R x A(n) is a dila tion of Arveson's spectral algebra C*(E-n) which is thus also KK-contractib le. We show that E subset of M(C*(E)) in many cases. The computation of gen erators shows the existence of nontrivial projections in C*(E-n) which impl ies them being simple nuclear infinite and KK-contractible.