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3 votes
0 answers
109 views

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 ...
Tomás Pacheco's user avatar
3 votes
1 answer
285 views

Extreme points of the set of all traces

Let $G$ be a finitely generated group with a bound on its complex unitary irreducible representations: That is assume all complex unitary irreducibles of $G$ have degrees at most $k$ for some integer $...
user3826143's user avatar
9 votes
0 answers
267 views

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' ...
Tomasz Kania's user avatar
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0 votes
2 answers
231 views

rank 1 projections of finite dimensional von Neumann algebra have the same traces?

Let M be a finite dimensional von Neumann algebras with a normal faithful trace. Let e and f be two projections with rank 1. I want to know if e and f have identical traces. (This is obviously true if ...
user83971's user avatar