3 problems

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Conjecture on conjugation-invariant matrix representations of truncated Toeplitz operators
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…
Conjectureopencomplex-symmetric-matrices operator-theory truncated-toeplitz-operatorsarXiv posted 2 days ago
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The $C_{\theta}$ -real matrix representation conjecture for truncated Toeplitz operators
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…
Problemopencomplex-symmetric-matrices model-spaces truncated-toeplitz-operatorsarXiv posted 2 days ago
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Conjecture on rank-two partial isometries being unitarily equivalent to complex symmetric matrices
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…
Conjectureopencomplex-symmetric-matrices operator-theory partial-isometriesarXiv posted 2 days ago

Conjecture on conjugation-invariant matrix representations of truncated Toeplitz operators