Added elementary properties of adjoint maps.
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Bokuan Li
2026-08-08 19:39:18 -04:00
parent ae2fc8147f
commit 1bc1b17fee
3 changed files with 77 additions and 1 deletions

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@@ -13,7 +13,7 @@ Depending on the topology placed on $H \otimes H$, and the corresponding complet
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 \textbf{ultraweak}/\textbf{$\sigma$-weak} topology on $B(H)$.
\end{definition}
\begin{proof}
By \autoref{proposition:projective-tensor-product-dual}.
By \autoref{proposition:projective-tensor-product-dual} and the \hyperref[Riesz Representation Theorem]{theorem:riesz-hilbert}.
\end{proof}
Seeing that $B(H)$ is a dual Banach space, the following fact is immediate: