Dynamical systems and commutants in crossed products
(2007) In International Journal of Mathematics 18(4). p.455471 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 semisimple 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 semisimple 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:
https://lup.lub.lu.se/record/939211
 author
 Silvestrov, Sergei ^{LU} ; Svensson, Christian and de Jeu, Marcel
 organization
 publishing date
 2007
 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 Publishing
 external identifiers

 wos:000251316300005
 scopus:34249102837
 ISSN
 0129167X
 DOI
 10.1142/S0129167X07004217
 project
 Noncommutative Analysis of Dynamics, Fractals and Wavelets
 language
 English
 LU publication?
 yes
 id
 6c8df0199da5496c8f96da6d796ba188 (old id 939211)
 alternative location
 http://www.worldscinet.com/cgibin/details.cgi?id=pii:S0129167X07004217&type=html
 date added to LUP
 20160401 16:49:52
 date last changed
 20210106 07:07:48
@article{6c8df0199da5496c8f96da6d796ba188, 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 semisimple 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 = {0129167X}, language = {eng}, number = {4}, pages = {455471}, publisher = {World Scientific Publishing}, series = {International Journal of Mathematics}, title = {Dynamical systems and commutants in crossed products}, url = {http://dx.doi.org/10.1142/S0129167X07004217}, doi = {10.1142/S0129167X07004217}, volume = {18}, year = {2007}, }