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*-semigroup endomorphisms of B(H)

Lajos Molnar
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Abstract

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

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Lajos Molnar. 2000-05-17. *-semigroup endomorphisms of B(H). https://arxiv.org/abs/math/0005167

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