Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball

Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball

We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Ban...

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Main Authors: Alma García, Nikolai Vasilevski
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2015/306168
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spelling doaj-a31034b1c1194e17a2dc03c77bc94ed42020-11-24T22:43:56ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/306168306168Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit BallAlma García0Nikolai Vasilevski1Department of Mathematics, CINVESTAV, Mexico City 07360, MexicoDepartment of Mathematics, CINVESTAV, Mexico City 07360, MexicoWe extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.http://dx.doi.org/10.1155/2015/306168
collection DOAJ
language English
format Article
sources DOAJ
author Alma García
Nikolai Vasilevski
spellingShingle Alma García
Nikolai Vasilevski
Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball
Journal of Function Spaces
author_facet Alma García
Nikolai Vasilevski
author_sort Alma García
title Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball
title_short Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball
title_full Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball
title_fullStr Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball
title_full_unstemmed Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball
title_sort toeplitz operators on the weighted bergman space over the two-dimensional unit ball
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2015-01-01
description We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.
url http://dx.doi.org/10.1155/2015/306168
work_keys_str_mv AT almagarcia toeplitzoperatorsontheweightedbergmanspaceoverthetwodimensionalunitball
AT nikolaivasilevski toeplitzoperatorsontheweightedbergmanspaceoverthetwodimensionalunitball
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