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

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

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