Hyponormality on a Weighted Bergman Space

Hyponormality on a Weighted Bergman Space

A bounded Hilbert space operator T is hyponormal if T∗T−TT∗ is a positive operator. We consider the hyponormality of Toeplitz operators on a weighted Bergman space. We find a necessary condition for hyponormality in the case of a symbol of the form f+g¯ where f and g are bounded analytic functions o...

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Main Authors: Houcine Sadraoui, Borhen Halouani, Mubariz T. Garayev, Adel AlShehri
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/8398012
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spelling doaj-003a6761464b46b597f969cfdccb82d52020-11-25T03:26:37ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/83980128398012Hyponormality on a Weighted Bergman SpaceHoucine Sadraoui0Borhen Halouani1Mubariz T. Garayev2Adel AlShehri3Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaA bounded Hilbert space operator T is hyponormal if T∗T−TT∗ is a positive operator. We consider the hyponormality of Toeplitz operators on a weighted Bergman space. We find a necessary condition for hyponormality in the case of a symbol of the form f+g¯ where f and g are bounded analytic functions on the unit disk. We then find sufficient conditions when f is a monomial.http://dx.doi.org/10.1155/2020/8398012
collection DOAJ
language English
format Article
sources DOAJ
author Houcine Sadraoui
Borhen Halouani
Mubariz T. Garayev
Adel AlShehri
spellingShingle Houcine Sadraoui
Borhen Halouani
Mubariz T. Garayev
Adel AlShehri
Hyponormality on a Weighted Bergman Space
Journal of Function Spaces
author_facet Houcine Sadraoui
Borhen Halouani
Mubariz T. Garayev
Adel AlShehri
author_sort Houcine Sadraoui
title Hyponormality on a Weighted Bergman Space
title_short Hyponormality on a Weighted Bergman Space
title_full Hyponormality on a Weighted Bergman Space
title_fullStr Hyponormality on a Weighted Bergman Space
title_full_unstemmed Hyponormality on a Weighted Bergman Space
title_sort hyponormality on a weighted bergman space
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2020-01-01
description A bounded Hilbert space operator T is hyponormal if T∗T−TT∗ is a positive operator. We consider the hyponormality of Toeplitz operators on a weighted Bergman space. We find a necessary condition for hyponormality in the case of a symbol of the form f+g¯ where f and g are bounded analytic functions on the unit disk. We then find sufficient conditions when f is a monomial.
url http://dx.doi.org/10.1155/2020/8398012
work_keys_str_mv AT houcinesadraoui hyponormalityonaweightedbergmanspace
AT borhenhalouani hyponormalityonaweightedbergmanspace
AT mubariztgarayev hyponormalityonaweightedbergmanspace
AT adelalshehri hyponormalityonaweightedbergmanspace
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