*-semigroup endomorphisms of B(H)

Details *-semigroup endomorphisms of B(H) *-semigroup endomorphisms of B(H)

2000-05-17

arxiv.org/abs/math/0005167v1

Mathematics

Operator Algebras

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

Scientific paper

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.

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