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Dynamical Systems Associated with Crossed Products

Svensson, Christian LU ; Silvestrov, Sergei LU and de Jeu, M. (2009) In Acta Applicandae Mathematicae 108(3). p.547-559
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)
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author
organization
publishing date
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
0167-8019
DOI
10.1007/s10440-009-9506-5
language
English
LU publication?
yes
id
0b3542e1-e0cf-4425-ae62-9442e133a895 (old id 2799104)
date added to LUP
2012-06-19 11:35:02
date last changed
2017-02-26 03:52:59
@article{0b3542e1-e0cf-4425-ae62-9442e133a895,
  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         = {0167-8019},
  keyword      = {Crossed product,Banach algebra,Ideal,Dynamical system,Maximal,Abelian subalgebra,ALGEBRAS},
  language     = {eng},
  number       = {3},
  pages        = {547--559},
  publisher    = {Springer},
  series       = {Acta Applicandae Mathematicae},
  title        = {Dynamical Systems Associated with Crossed Products},
  url          = {http://dx.doi.org/10.1007/s10440-009-9506-5},
  volume       = {108},
  year         = {2009},
}