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arXiv · 2503.14200

Commutants of a certain class of Toeplitz operators

Aissa Bouhali·Issam Louhichi·Abdel Rahman Yousef
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Abstract

A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute with it. In this paper, we provide a complete description of bounded Toeplitz operators $T_f$, where the symbol $f$ has a truncated polar decomposition, that commute with a Toeplitz operator whose symbol is the sum of a quasihomogeneous function and a bounded analytic function.

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Aissa Bouhali, Issam Louhichi, Abdel Rahman Yousef. 2025-03-18. Commutants of a certain class of Toeplitz operators. https://arxiv.org/abs/2503.14200

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