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Dynamical Systems and Commutants in Crossed Products

Christian Svensson·Sergei Silvestrov·Marcel de Jeu
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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.

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Christian Svensson, Sergei Silvestrov, Marcel de Jeu. 2006-04-27. Dynamical Systems and Commutants in Crossed Products. https://doi.org/10.1142/s0129167x07004217

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