Cocycles for one-parameter flows of B(h)

摘要

The set of local cocycles is a natural invariant for an E-0-semigroup. It has a multiplicative structure, as well as a partial order structure among its positive elements. In particular, the unitary local cocycles form a topological group which may be appropriately viewed as the automorphism. group of the E-0-semigroup, while the set of positive contractive local cocycles is order isomorphic to the set of flows of completely positive maps dominated by the semigroup. The local cocycles have been computed for the standard, type I examples of the CAR/CCR flows by W. Arveson and R. Bhat. In this paper, we compute for the first time the local cocycles for a class of type II Eo-semigroups of B(h) with index zero, and describe the order structure as well as the multiplication in terms of the boundary weight associated with such a semigroup. (c) 2005 Elsevier Inc. All rights reserved.