All Questions

I asked this 11 days ago at MSE, but there was no answer, I hope people here could help. Let $G$ be a locally compact group, and $X$ a Hilbert space. A unitary representation $\varphi:G\to B(X)$ is ...

Let $G$ be a locally compact group, $C_0(G)$ the $C^*$-algebra of continuous functions on $G$ that vanish at infinity, $C_b(G)$ the $C^*$-algebra of bounded continuous functions on $G$. We know that $...

Let $G$ be a compact group and $u: G \to B(H)$ be a strongly continuous unitary representation on the Hilbert space $H$. Then is $u: G \to B(H)$ strictly continuous? That is, give $B(H)$ the topology ...

Recall that a locally compact group $G$ is said to be an $[FC]^-$ group, if each conjugacy class in $G$ has a compact closure; an $[SIN]$ group, if each neighborhood of the identity includes a ...