Semisimplicity and Semi-crossed Products
by
Allan Donsig
University of Nebraska-Lincoln
Coauthors: Aristides Katavolos (University of Athens)

Suppose X is a locally compact Hausdorff space, \phi: X --> X is a proper, continuous surjection, and construct the semi-crossed product C₀(X) ×_\alpha Z⁺ given by \alpha(f)=f o \phi^-1 Characterizing which of these operator algebras are semisimple has attracted some interest, including work by Muhly, by Peters, and by Mastranglo, Muhly, and Solel. We show that the semi-crossed product is semisimple if and only if the recurrent points of \phi are dense in X.

Date received: April 27, 1999