Logo image
Automorphism Groups and Invariant Subspace Lattices
Journal article   Open access   Peer reviewed

Automorphism Groups and Invariant Subspace Lattices

Paul S. Muhly and Baruch Solel
Transactions of the American Mathematical Society, Vol.349(1), pp.311-330
01/01/1997
DOI: 10.1090/S0002-9947-97-01755-8
url
https://doi.org/10.1090/S0002-9947-97-01755-8View
Published (Version of record) Open Access

Abstract

Let (B, R, α) be a C*- dynamical system and let A = Bα([0, ∞)) be the analytic subalgebra of B. We extend the work of Loebl and the first author that relates the invariant subspace structure of π(A), for a C*representation π on a Hubert space π, to the possibility of implementing a on π. We show that if π is irreducible and if lat π(A) is trivial, then π(A) is ultraweakly dense in ( π). We show, too, that if A satisfies what we call the strong Dirichlet condition, then the ultraweak closure of π(A) is a nest algebra for each irreducible representation π. Our methods give a new proof of a "density" theorem of Kaftal, Larson, and Weiss and they sharpen earlier results of ours on the representation theory of certain subalgebras of groupoid C*-algebras.
Research article

Details

Metrics

Logo image