2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155765For 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.9 pagesFunctional Analysis47B35text