AF-subalgebras of a C*-algebra generated by a mapping

Abstract

In this paper we consider a C*-subalgebra of the algebra of all bounded operators B(l2(X)) on the Hilbert space l2(X)) with one generating element T φ induced by a mapping φ of a set X into itself. We prove that such a C*-algebra has an AF-subalgebra and establish commutativity conditions for the latter. We prove that a C*-algebra generated by a mapping produces a dynamic system such that the corresponding group of automorphisms is invariant on elements of the AF- subalgebra. © 2010 Allerton Press, Inc.