All Questions

Does a robust version of Schur's lemma exist? Specifically, I was wondering about something like this: Let $B$ be a bounded operator over a vector space $V$, with underlying field $\mathbb{C}$ and ...

Let $\mathcal{A}$ be a semisimple $\mathbb{C}$-algebra. By the Artin-Wedderburn theorem, it is isomorphic to a direct product of matrix algebras: $$ \mathcal{A} = \prod_{i=1}^m M_{n_i}(\mathbb{C})$$ ...

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, ...

Motivated by this question and its great answers, I become very curious to know what do we know about RFD (residually finite dimensional) groups and $C^*$-algebras, e.g. do we know how these ...

Let $G$ be a group, and consider the matrix elements of finite dimensional irreducible unitary representations of $G$ over $\mathbb{C}$ as functions $f:G\to \mathbb{C}$. If $G$ is finite, any two ...

If $\mathscr{X}$ is a Hilbert space, we denote by $\mathrm{GL}(\mathscr{X})$ the group of all bounded operators on $\mathscr{X}$ with bounded inverses. Let $\mathbb{F}_2$ be the free group on two ...