Course related house keeping.

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Bokuan Li
2026-11-06 15:52:00 -05:00
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\section{Injective Operator Systems}
\label{section:injective-ops}
By \hyperref[Arveson's Extension Theorem]{theorem:arveson-extension}, $B(H)$ is injective for any Hilbert space $H$. Further, the \hyperref[Choi-Effros Theorem]{choi-effros} implies that every operator system embeds into $B(H)$, for a suitable Hilbert space $H$. Therefore the category of operator systems, with unital complete order isomorphisms, has sufficiently many injectives.
\begin{theorem}
\label{theorem:opsys-predual}
Let $S, T$ be operator systems. If $T$ admits a predual, then the space
\[
UCP(S; T) = \bracsn{\phi: S \to T| \phi \text{ unital, completely positive}}
\]
is compact in the point-weak* topology.
\end{theorem}
\begin{definition}[Injective]
\label{definition:injective-operator-system}
Let
\end{definition}