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arXiv · 2501.14069

Bounded Toeplitz Products on the Hardy Space

Ryan O'Loughlin
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Abstract

A Toeplitz operator on the Hardy space of the unit circle is bounded if and only if its symbol is bounded. For two Toeplitz operators, there are no known function-theoretic conditions for their symbols, which are equivalent to the product of the Toeplitz operators being bounded. In this paper, we provide a solution to this problem, by showing under certain assumptions that the product of two Toeplitz operators is bounded if and only if the product of their symbols is bounded.

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Ryan O'Loughlin. 2025-01-23. Bounded Toeplitz Products on the Hardy Space. https://arxiv.org/abs/2501.14069

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