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arXiv · 1707.09677

Hyponormal Toeplitz operators with non-harmonic symbol acting on the Bergman space

Matthew Fleeman·Constanze Liaw
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Abstract

The Toeplitz operator acting on the Bergman space $A^{2}(\mathbb{D})$, with symbol $\varphi$ is given by $T_{\varphi}f=P(\varphi f)$, where $P$ is the projection from $L^{2}(\mathbb{D})$ onto the Bergman space. We present some history on the study of hyponormal Toeplitz operators acting on $A^{2}(\mathbb{D})$, as well as give results for when $\varphi$ is a non-harmonic polynomial. We include a first investigation of Putnam's inequality for hyponormal operators with non-analytic symbols. Particular attention is given to unusual hyponormality behavior that arises due to the extension of the class of allowed symbols.

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Matthew Fleeman, Constanze Liaw. 2017-07-30. Hyponormal Toeplitz operators with non-harmonic symbol acting on the Bergman space. https://doi.org/10.7153/oam-2019-13-04

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