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

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dc.creatorLe, Trieu
dc.date2008-02-26
dc.date.accessioned2026-07-07T09:23:32Z
dc.date.available2026-07-07T09:23:32Z
dc.descriptionFor 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.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0802.3925
dc.identifierhttp://arxiv.org/abs/0802.3925
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155765
dc.subjectFunctional Analysis
dc.subject47B35
dc.titleA refined Luecking's theorem and finite-rank products of Toeplitz operators
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