All Questions
3 questions
5
votes
2
answers
418
views
Is the left-regular representation of a locally compact group a homeomorphism onto its image?
Consider the left-regular representation $\lambda : G \to B(L^2(G))$, $\lambda_g f(h) = f(g^{-1}h)$, for a locally compact group.
It is well-known that this is a unitary faithful and strongly-...
5
votes
1
answer
165
views
Is norm-continuous representation factored through a Lie quotient group?
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 ...
2
votes
0
answers
157
views
Primitive ideal space and unitary dual of a [SIN] group - when are they Hausdorff?
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 ...