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, MÜBARİZ TAPDIGOĞLU and GÜRDAL, MEHMET
(2018)
"Remarks on the zero Toeplitz product problem in the Bergman and Hardy spaces,"
Turkish Journal of Mathematics: Vol. 42:
No.
3, Article 59.
https://doi.org/10.3906/mat-1706-93
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss3/59
