Definition 37.1.1 (Ultraweak Topology).label Let $H$ be a complex Hilbert space, then the dual of $H \wh \otimes_{\pi} H$ is $B(H)$, and the $\sigma(B(H), H \wh \otimes_{\pi} H)$-topology is the ultraweak/$\sigma$-weak topology on $B(H)$.
Proof. By Proposition 13.11.2 and the Riesz Representation Theorem.$\square$
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