3 problems

A $*$-extendible representation $\sigma$ of ${\mathfrak{A}}_n$ is called regular when its absolutely continuous and type L parts coincide. Regularity conjecture. Every representati…

Let $S=[S_1\,\cdots\,S_n]$ be an isometric $n$-tuple on a Hilbert space ${\mathcal{H}}$, meaning that $S_i^*S_j=\delta_{i,j}I$ for $i,j=1,\ldots,n$. A free semigroup algebra…

Davidson–Li–Pitts conjecture. For $n\geq2$, every absolutely continuous representation of $\mathcal{A}_{n}$ is of type L.