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Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry

3 votes
1 answer
498 views

Is there a link between $H_2(G,\mathbb{Z})$, the Schur Multiplier of a group, and the "other...

The name for the the following 2 mathematical objects: $$H_2(G,\mathbb{Z})$$ and $$\{K:G\times G\longrightarrow\mathbb{C}\ |\ \forall T\in B(l^2(G))\text{we have that}~S:G\times G\longrightarrow\ma …
5 votes
0 answers
317 views

Unitary representations of Tarski Monsters and other beasts

Did people study the unitary representations of Tarsky Monsters, for example the ones constructed by Ol'shanskii? Are there any exotic representations, ie. except the ones related to the left regular, …
6 votes
0 answers
497 views

Faithful and weakly-mixing representations of Property (T) groups in relation to left regula...

Is it known that: Any countable Property (T) group (or more generally, a non-amenable group) has a faithful, weakly-mixing representation which is NOT weakly included in its left regular representatio …
3 votes
1 answer
165 views

Sets $E$ in $\mathbb{Z}$ such that any $l^2$ function with support on $E$ comes from Fourier...

Are there infinite sets $E\subset\mathbb{Z}$ such that any $f\in l^2(\mathbb{Z})$ with support on $E$ comes from the Fourier transform of a continuous function on $\mathbb{T}$ ? If yes, is there a cha …