6
votes
2answers
258 views

Are the reduced group Von Neumann algebra/ Group $C^{\ast}$ algebra functorial in the case of LCH groups

Let $G$ be a LCH group and $\mu$ be its left Haar measure. Call $\lambda_G : G \to U(L_2(G,\mu))$ the left regular representation. We can define the reduced $C^{\ast}$ algebra and reduced Von Neumann ...
1
vote
0answers
162 views

From positive definite function to Følner sequence --— a question on amenability and nuclearity

We know that amenability of countable discrete group $\Gamma$ has many equivalent characterizations. In particular, there are two: a) there is a sequence of finitely supported positive definite ...
2
votes
1answer
627 views

Where is the error in this argument?

Let $G$ be a locally compact Hausdorff group. It is known that $G$ can be topologically embedded in $W^{\ast}(G)$ , its universal $W^{\ast}$-algebra (with the $\sigma$-weak topology). An element $T ...
3
votes
1answer
360 views

Are the categories of representations of G and C*(G) isomorphic?

Let G be a locally compact Hausdorff group, and C*(G) the full group C* algebra. I found in some books that "representation theory of both is the same". Can this be expressed as "the categories are ...