A refined Luecking's theorem and finite-rank products of Toeplitz operators

Trieu Le

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arXiv · 0802.3925

A refined Luecking's theorem and finite-rank products of Toeplitz operators

Trieu Le

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Abstract

For any function $f$ in $L^{\infty}(\mathbb{D})$, let $T_f$ denote the corresponding Toeplitz operator the Bergman space $A^2(\mathbb{D})$. A recent result of D. Luecking shows that if $T_f$ has finite rank then $f$ must be the zero function. Using a refined version of this result, we show that if all except possibly one of the functions $f_1,..., f_{m}$ are radial and $T_{f_1}... T_{f_m}$ has finite rank, then one of these functions must be zero.

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BibTeX RIS

Trieu Le. 2008-02-26. A refined Luecking's theorem and finite-rank products of Toeplitz operators. https://arxiv.org/abs/0802.3925

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