| Title | Dynamical systems and commutants in crossed products |
| Authors | Sergei Silvestrov, Christian Svensson, Marcel de Jeu |
| Alternative Location | http://www.worldscinet.com/..., Restricted Access |
| Alternative Location | http://dx.doi.org/10.1142/S..., Restricted Access |
| Publication | International Journal of Mathematics |
| Year | 2007 |
| Volume | 18 |
| Issue | 4 |
| Pages | 455 - 471 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | World Scientific |
| Abstract English | 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. |
| Keywords | maximal abelian subalgebra, Crossed product, completely regular Banach algebra, dynamical system, |
| ISBN/ISSN/Other | ISSN: 0129-167X |
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