Dynamical Systems Associated with Crossed Products
(2009) In Acta Applicandae Mathematicae 108(3). p.547559 Abstract
 In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C (*)algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new... (More)
 In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C (*)algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A'. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2799104
 author
 Svensson, Christian ^{LU} ; Silvestrov, Sergei ^{LU} and de Jeu, M.
 organization
 publishing date
 2009
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Crossed product, Banach algebra, Ideal, Dynamical system, Maximal, Abelian subalgebra, ALGEBRAS
 in
 Acta Applicandae Mathematicae
 volume
 108
 issue
 3
 pages
 547  559
 publisher
 Springer
 external identifiers

 wos:000271941500006
 scopus:71449105220
 ISSN
 01678019
 DOI
 10.1007/s1044000995065
 language
 English
 LU publication?
 yes
 id
 0b3542e1e0cf4425ae629442e133a895 (old id 2799104)
 date added to LUP
 20160401 13:50:52
 date last changed
 20210922 02:18:27
@article{0b3542e1e0cf4425ae629442e133a895, abstract = {In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C (*)algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A'. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system.}, author = {Svensson, Christian and Silvestrov, Sergei and de Jeu, M.}, issn = {01678019}, language = {eng}, number = {3}, pages = {547559}, publisher = {Springer}, series = {Acta Applicandae Mathematicae}, title = {Dynamical Systems Associated with Crossed Products}, url = {http://dx.doi.org/10.1007/s1044000995065}, doi = {10.1007/s1044000995065}, volume = {108}, year = {2009}, }