Bounded Toeplitz Products on the Hardy Space
Functional Analysis
2025-01-30 v2
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.
Cite
@article{arxiv.2501.14069,
title = {Bounded Toeplitz Products on the Hardy Space},
author = {Ryan O'Loughlin},
journal= {arXiv preprint arXiv:2501.14069},
year = {2025}
}