Definition 37.4.1 (Separating Vector).label Let $H$ be a complex Hilbert space, $A \subset B(H)$, and $x \in H$, then $x$ is a separating vector for $A$ if the mapping $A \to H$ defined by $T \mapsto Tx$ is injective.
Definition 37.4.1 (Separating Vector).label Let $H$ be a complex Hilbert space, $A \subset B(H)$, and $x \in H$, then $x$ is a separating vector for $A$ if the mapping $A \to H$ defined by $T \mapsto Tx$ is injective.
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