On the Banach *algebra crossed product associated with a topological dynamical system
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Abstract
Given a topological dynamical system Sigma = (X, sigma), where X is a compact Hausdorff space and a a homeomorphism of X, we introduce the Banach *algebra crossed product l(1) (E) most naturally associated with Sigma and initiate its study. It has a richer structure than its well investigated C*envelope, as becomes evident from the possible existence of nonselfadjoint closed ideals. We link its ideal structure to the dynamics, determining when the algebra is simple, or prime, and when there exists a nonselfadjoint closed ideal. A structure theorem is obtained when X consists of one finite orbit, and the algebra is shown to be Hermitian if X is finite. The key lies in analysing the commutant of C(X) in the algebra, which is shown to be a maximal abelian subalgebra with nonzero intersection with each nonzero closed ideal. (C) 2012 Elsevier Inc. All rights reserved.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY
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Original language  English 

Pages (fromto)  47464765 
Journal  Journal of Functional Analysis 
Volume  262 
Issue number  11 
Publication status  Published  2012 
Publication category  Research 
Peerreviewed  Yes 