Endomorphisms of certain operator algebras (Q916059)

Let B(H) be the algebra of all bounded operators on a Hilbert space H, and let A be the \(C^*\)-algebra C(X,B(H)) for a compact space X. Generalizing a definition of \textit{R. T. Powers} [Can. J. Math. 40, 86-114 (1988; Zbl 0632.46058)], the author introduces the notion of a C(X)-shift for *-endomorphisms of A. He proves for C(X)-shifts an analogue of a theorem of \textit{E. C. Lance} [Am. J. Math. 91, 160-174 (1969; Zbl 0177.176)] on locally inner C(X)-automorphisms of A. Moreover, he gives an example of a C(X)-shift \(\sigma\) such that not all induced endomorphisms \(\sigma_ x\), \(x\in X\), are shifts of B(H).