ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46, 47 Amosov, Grigori, Moscow Institute of Physics and Technology, Russia: Cocycle conjugacy classes of Powers’ semiflow of shifts Let A(h) be the algebra of the canonical anticommutation relations over the separable Hilbert space h and let ω_{ν} be a quasifree state on A(h) with defining twopoint function ω_{ν}(a^{∗}(f)a(g)) = ν(g, f), g, f ∈ h, 0 < ν ≤ 1/2. The GNS representation π_{ν} associated with ω_{ν} generates the hyperfinite factor M_{ν} = π_{ν}(A(h))′′ of type II_{1} in the case of ν = 1/2 and of type III_{λ} otherwise. Every C_{0}-semigroup of isometries V in h generates an E_{0}-semigroup B_{ν}(V) on M_{ν}. In case V consists of completely nonunitary isometries, B_{ν}(V) is Powers’ semiflow of shifts. Theorem. Given a C_{0}-semigroup of isometries V with uniformly continuous unitary part there is a C_{0}-semigroup of completely nonunitary isometries S such that the E_{0}-semigroup B_{ν}(V) is cocycle conjugate to Powers’ semiflow of shifts B_{ν}(S). Ref. G. Amosov, On cocycle conjugacy classes of quasifree K-systems, In: “Some probl. of fund. and appl. math. ”, Moscow Inst. Phys. and Tech.,