On the growth of resolvent of Toeplitz operators

Leonid Golinskii; Stanislas Kupin; Anna Vishnyakova

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arXiv · 2401.12095

On the growth of resolvent of Toeplitz operators

Leonid Golinskii·Stanislas Kupin·Anna Vishnyakova

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Abstract

We study the growth of the resolvent of a Toeplitz operator $T_b$, defined on the Hardy space, in terms of the distance to its spectrum $\sigma(T_b)$. We are primarily interested in the case when the symbol $b$ is a Laurent polynomial (\emph{i.e., } the matrix $T_b$ is banded). We show that for an arbitrary such symbol the growth of the resolvent is quadratic, and under certain additional assumption it is linear. We also prove the quadratic growth of the resolvent for a certain class of non-rational symbols.

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Leonid Golinskii, Stanislas Kupin, Anna Vishnyakova. 2024-01-22. On the growth of resolvent of Toeplitz operators. https://arxiv.org/abs/2401.12095

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