Endomorphisms of Certain Operator Algebras

Abstract

In this paper we study C(X)-endomorphisms of C(X, \mathfrak{B}(\mathfrak{H})), for X a compact space. The local structure of these endomorphisms is analyzed. We prove the existence of a C(X)-shift, not all of whose fibers are shifts on \mathfrak{B}(\mathfrak{H}).