Turkish Journal of Mathematics
Abstract
In this article, we are interested in the zero Toeplitz product problem: for two symbols $f,g\in L^{\infty}\left( \mathbb{D},dA\right) ,$\ if the product $T_{f}T_{g}$\ is identically zero on $L_{a}^{2}\left( \mathbb{D}\right), $\ then can we claim $T_{f}$\ or $T_{g}$\ is identically zero? We give a particular solution of this problem. A new proof of one particular case of the zero Toeplitz product problem in the Hardy space $H^{2}\left( \mathbb{D}% \right) $ is also given.
DOI
10.3906/mat-1706-93
Keywords
Toeplitz operator, Bergman space, Hardy space, zero Toeplitz product, Berezin symbol
First Page
1504
Last Page
1508
Recommended Citation
GARAYEV, M. T, & GÜRDAL, M (2018). Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces. Turkish Journal of Mathematics 42 (3): 1504-1508. https://doi.org/10.3906/mat-1706-93
