- Turkish Journal of Mathematics
- Vol: 42 Issue: 3
- Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces
Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces
Authors : Mübariz Tapdigoğlu Garayev, Mehmet Gürdal
Pages : 1504-1508
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Toeplitz operator, Bergman space, Hardy space, zero Toeplitz product, Berezin symbol