Mathematics – Dynamical Systems
Scientific paper
2006-04-27
Internat. J. Math. 18 (2007), 455--471
Mathematics
Dynamical Systems
14 pages. Minor misprints corrected and text improvements made
Scientific paper
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.
Jeu Marcel de
Silvestrov Sergei
Svensson Christian
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