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Faithful traces on reduced $C^*$-algebra of a measured groupoid
Let $G$ be a measured étale groupoid with quasi-invariant measure $\mu$ (that induces the reduced $C^* $-algebra, meaning it has full support) with associated equivalent measures $\nu,\nu^{-1}$.
Is ...
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Can we extend c.p. normal maps on a finite von Neumann algebra $M$ to $L_0(M)_+$?
Suppose that $M$ is a von Neumann algebra with a finite, normal, faithful trace $\tau$. Let $T\colon M\to M$ be a completely positive, normal map.
Can $T$ be extended to a `positively linear map' ...