Journal article
Automorphism Groups and Invariant Subspace Lattices
Transactions of the American Mathematical Society, Vol.349(1), pp.311-330
01/01/1997
DOI: 10.1090/S0002-9947-97-01755-8
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.
Details
- Title: Subtitle
- Automorphism Groups and Invariant Subspace Lattices
- Creators
- Paul S. Muhly - University of Iowa, MathematicsBaruch Solel - Technion – Israel Institute of Technology
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.349(1), pp.311-330
- DOI
- 10.1090/S0002-9947-97-01755-8
- ISSN
- 0002-9947
- eISSN
- 1088-6850
- Publisher
- American Mathematical Society
- Number of pages
- 20
- Language
- English
- Date published
- 01/01/1997
- Academic Unit
- Statistics and Actuarial Science; Mathematics
- Record Identifier
- 9984083227402771
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