Dynamical systems and commutants in crossed products
(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:
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
- 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
- 2016-04-01 16:49:52
- date last changed
- 2022-03-30 18:37:52
@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}},
keywords = {{maximal abelian subalgebra; Crossed product; completely regular Banach algebra; dynamical system}},
language = {{eng}},
number = {{4}},
pages = {{455--471}},
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}},
}