Continuity of CP-semigroups in the point-strong operator topology

Abstract

We prove that if $\{{\varphi }_t{\}}_{t\ge 0}$ is a CP-semigroup acting on a von Neumann algebra $M\subseteq B(H)$, then for every $A\in M$ and $\xi \in H$, the map $t\mapsto {\varphi }_t(A)\xi$ is norm-continuous. We discuss the implications of this fact to the existence of dilations of CP-semigroups to semigroups of endomorphisms.

7 pages

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