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arXiv · 2605.02186

Subnormal block Toeplitz operators

Mankunikuzhiyil Abhinand·Raul E. Curto·In Sung Hwang·Woo Young Lee·Thankarajan Prasad
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Abstract

In this paper we consider the subnormality of block Toeplitz operators $T_\Phi$, where $\Phi$ is an $n\times n$ matrix-valued function on the unit circle $\mathbb T$ of the form $$ \Phi=Q\Phi^* \quad \hbox{($Q$ is a finite Blaschke--Potapov product).} $$ This is related to a matrix-valued version of Halmos's Problem 5 and Nakazi-Takahashi Theorem. We ask whether $T_\Phi$ is either normal or analytic if $T_\Phi$ is subnormal, where $\Phi$ is of the above form. We give answers to this problem for different cases of the symbol. Moreover, we provide a sufficient condition for the answer to be affirmative when $\Phi^*$ is not of bounded type.

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Mankunikuzhiyil Abhinand, Raul E. Curto, In Sung Hwang, Woo Young Lee, Thankarajan Prasad. 2026-05-04. Subnormal block Toeplitz operators. https://doi.org/10.1007/s11854-025-0358-3

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