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

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

2008-02-26

arxiv.org/abs/0802.3925v1

Mathematics

Functional Analysis

9 pages

Scientific paper

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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