*-semigroup endomorphisms of B(H)

Abstract

Let H be a complex infinite dimensional Hilbert space. We describe the form of all *-semigroup endomorphisms $\varphi$ of B(H) which are uniformly continuous on every commutative C*-subalgebra. In particular, we obtain that if $\varphi$ satisfies $\varphi (0)=0$, then $\varphi$ is additive.

7 pages. To appear in the Proceedings of the Memorial Conference for Bela Szokefalvi-Nagy, 1999, Szeged, Hungary