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 $\mathfrak{B}(\mathfrak{H})$.