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Dynamical systems and commutants in crossed products

Silvestrov, Sergei LU ; Svensson, Christian and de Jeu, Marcel (2007) In International Journal of Mathematics 18(4). p.455-471
Abstract
In this paper, we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X. The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where these conditions can be shown to be equivalent to a condition in topological dynamics. As a further step, using the Gelfand transform, we obtain for a commutative completely regular semi-simple Banach algebra a topological dynamical condition on its character space which is equivalent to the algebra being maximal abelian in a crossed product with the... (More)
In this paper, we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X. The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where these conditions can be shown to be equivalent to a condition in topological dynamics. As a further step, using the Gelfand transform, we obtain for a commutative completely regular semi-simple Banach algebra a topological dynamical condition on its character space which is equivalent to the algebra being maximal abelian in a crossed product with the integers. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
maximal abelian subalgebra, Crossed product, completely regular Banach algebra, dynamical system
in
International Journal of Mathematics
volume
18
issue
4
pages
455 - 471
publisher
World Scientific
external identifiers
  • wos:000251316300005
  • scopus:34249102837
ISSN
0129-167X
DOI
10.1142/S0129167X07004217
project
Non-commutative Analysis of Dynamics, Fractals and Wavelets
language
English
LU publication?
yes
id
6c8df019-9da5-496c-8f96-da6d796ba188 (old id 939211)
alternative location
http://www.worldscinet.com/cgi-bin/details.cgi?id=pii:S0129167X07004217&type=html
date added to LUP
2008-01-21 15:53:29
date last changed
2017-02-26 04:17:25
@article{6c8df019-9da5-496c-8f96-da6d796ba188,
  abstract     = {In this paper, we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X. The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where these conditions can be shown to be equivalent to a condition in topological dynamics. As a further step, using the Gelfand transform, we obtain for a commutative completely regular semi-simple Banach algebra a topological dynamical condition on its character space which is equivalent to the algebra being maximal abelian in a crossed product with the integers.},
  author       = {Silvestrov, Sergei and Svensson, Christian and de Jeu, Marcel},
  issn         = {0129-167X},
  keyword      = {maximal abelian subalgebra,Crossed product,completely regular Banach algebra,dynamical system},
  language     = {eng},
  number       = {4},
  pages        = {455--471},
  publisher    = {World Scientific},
  series       = {International Journal of Mathematics},
  title        = {Dynamical systems and commutants in crossed products},
  url          = {http://dx.doi.org/10.1142/S0129167X07004217},
  volume       = {18},
  year         = {2007},
}