On the Banach *-algebra crossed product associated with a topological dynamical system
Research output: Contribution to journal › Article
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 non-self-adjoint closed ideals. We link its ideal structure to the dynamics, determining when the algebra is simple, or prime, and when there exists a non-self-adjoint 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 non-zero intersection with each non-zero closed ideal. (C) 2012 Elsevier Inc. All rights reserved.
|Research areas and keywords||
Subject classification (UKÄ) – MANDATORY
|Journal||Journal of Functional Analysis|
|Publication status||Published - 2012|