*-semigroup endomorphisms of B(H)

Abstract

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