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

2008/02/26 by Trieu Le, Le, Trieu
Mathematics · #47B35 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47B35

paper · pdf · doi:10.48550/arxiv.0802.3925

9 pages

arxiv created 2008/02/26 · arxiv updated 2009/12/01

Abstract

For any function f in L^∞(\mathbbD), let T_f denote the corresponding Toeplitz operator the Bergman space A²(\mathbbD). 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 f₁,..., f_m are radial and T_f1... T_fm has finite rank, then one of these functions must be zero.

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