Tagged Questions
1
vote
0answers
46 views
irreducible representation of a group
Reduced group $C^\ast$-algebra of group $G$ is defined to be $G^*_{r}(G)=\overline{\lambda(L^1(G))}$ where $\lambda$ is left regular representation. My question is how to get a irreducible ...
2
votes
0answers
57 views
Does a $C^*$ subalgebra of the centralizer of a unitary representation always contain the unit?
I am studying a theorem in Folland's "Course in Abstract Harmonic Analysis" where the following ingredients/assumptions are needed:
$G$ a locally compact group, $\pi$ a unitary representation of ...
0
votes
0answers
41 views
Representer theorem RKHS?
$\displaystyle\min_{f\in H_k} \gamma ||f||_{K}^2+f^TLf$
Given a RKHS $H_k$ does the representer theorem hold for this minimization problem over the function $f$? Here, $L$ is a fixed p.s.d ...
1
vote
1answer
115 views
A specific example of the GNS construction
In an introduction to the GNS construction, I'm told that the GNS construction is a generalization of the way that $L^{\infty} (X, \mu)$ has a representation on $L^2$ where $\mu$ is a measure on $X$. ...
6
votes
1answer
119 views
Why need two directions to make $\sim_{\rm wa}$ an equivalence relation?
Let $\pi$ and $\sigma$ be representations of a $C^*$-algebra $\mathcal{A}$. They are weak approximately equivalent ($\pi\mathbin{\sim_{\rm wa}}\sigma$) if there are sequences of unitary operators ...
4
votes
1answer
203 views
A particular (functional) determinant calculation
One wants to calculate the quantity, $\det'(\frac{\partial}{\partial t} - i [\alpha, ])$ where the prime on the "det" means that one wants to do a product over only non-zero eigenvalues of the ...
4
votes
1answer
131 views
Free groups and Kazhdan's property (T)
Showing non-amenability of a (non-abelian) free group is somewhat easy and one can do this immediately after the definition of amenability.
Is there an easy proof of the fact that free groups do not ...
6
votes
1answer
155 views
Topology on the tensor product of two topological vector spaces — how properties does it maintains?
Good morning, this is my first question in this website. If I have two topological vector spaces, say $A$ and $B$, I would like to know
1)how the topology on $A\otimes B$ is canonically defined?
...
4
votes
2answers
232 views
An hermitian operator problem
It is possible to have two hermitian operators $A$ et $B$, with :
$B^2 = \mathbb{I}d$
$[A,B] = i * \mathbb{I}d$
where $i$ is the usual (complex) square root of $(-1)$, and $\mathbb{I}d$ is the ...
3
votes
2answers
106 views
Extensions and Kazhdan's Property (T)
Is Kazhdan's property (T) stable under extensions? i.e. if $G$ is an extension of
a group with property (T) by a group with property (T), does it follow that $G$ has property (T)?
