Course related house keeping.
This commit is contained in:
@@ -0,0 +1,24 @@
|
||||
\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}
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user