3 problems

Let $M$ be a complex symmetric matrix, and suppose that $M$ is unitarily equivalent to a truncated Toeplitz operator (TTO). Let $B$ be an inner function, let $K_B$ be the correspon…

The $C_{\theta}$-real matrix representation conjecture. If $M$ is a complex symmetric matrix and is unitarily equivalent to a TTO, then there exist an inner function $u$ and a…

Let $T$ be a partial isometry on a $4$-dimensional complex Hilbert space, and suppose that $\operatorname{Rank} T=2$. A matrix $T$ is unitarily equivalent to a complex symmetric ma…