On the Banach *algebra crossed product associated with a topological dynamical system
(2012) In Journal of Functional Analysis 262(11). p.47464765 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... (More)
 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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2570834
 author
 de Jeu, Marcel; Svensson, Christian ^{LU} and Tomiyama, Jun
 organization
 publishing date
 2012
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Involutive Banach algebra, Crossed product, Ideal structure, Topological, dynamical system
 in
 Journal of Functional Analysis
 volume
 262
 issue
 11
 pages
 4746  4765
 publisher
 Elsevier
 external identifiers

 wos:000303087000005
 scopus:84859426221
 ISSN
 00221236
 DOI
 10.1016/j.jfa.2012.03.013
 language
 English
 LU publication?
 yes
 id
 561493d8ee784d128915d8d295a4f64c (old id 2570834)
 date added to LUP
 20120604 09:43:00
 date last changed
 20180107 07:06:47
@article{561493d8ee784d128915d8d295a4f64c, 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.}, author = {de Jeu, Marcel and Svensson, Christian and Tomiyama, Jun}, issn = {00221236}, keyword = {Involutive Banach algebra,Crossed product,Ideal structure,Topological,dynamical system}, language = {eng}, number = {11}, pages = {47464765}, publisher = {Elsevier}, series = {Journal of Functional Analysis}, title = {On the Banach *algebra crossed product associated with a topological dynamical system}, url = {http://dx.doi.org/10.1016/j.jfa.2012.03.013}, volume = {262}, year = {2012}, }