Flow under a function and discrete decomposition of properly infiniteW∗-algebras
W. J. Phillips · Pacific Journal of Mathematics · 1984
The purpose of this paper is to generalize the classical "flow under a function" construction to non-abelian W / *-algebras.That is, given an automorphism θ of a H / *-algebra N and a positive self-adjoint operator φ affiliated to the centre of N we show how to construct a continuous action a of the reals on a W*-algebra M. The resulting covariant system {M, a, R} is called the flow built on {N, θ, Z} under the function φ.PROPOSITION 2.2.Let {M,a,G} be a covariant system where G is abelian.Suppose that p -U p is a strongly continuous unitary representation of G in the centre of M such that a t (U p ) -(p, t)U p for all t E G and all p E G. Then there is an isomorphism K of (M, α, G} with [M a ® L°°(G), id ® σ, G} 5"wc/z /Λα/ K(Λ ) = x ® 1 /or x E M