Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space
We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-prod...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/578436 |
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| _version_ | 1832561202623938560 |
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| author | Jingyu Yang Liu Liu Yufeng Lu |
| author_facet | Jingyu Yang Liu Liu Yufeng Lu |
| author_sort | Jingyu Yang |
| collection | DOAJ |
| description | We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols. |
| format | Article |
| id | doaj-art-18f6da44b50a4260b23b2bb276cf0eba |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-18f6da44b50a4260b23b2bb276cf0eba2025-02-03T01:25:39ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/578436578436Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman SpaceJingyu Yang0Liu Liu1Yufeng Lu2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaWe study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols.http://dx.doi.org/10.1155/2013/578436 |
| spellingShingle | Jingyu Yang Liu Liu Yufeng Lu Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space Journal of Function Spaces and Applications |
| title | Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_full | Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_fullStr | Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_full_unstemmed | Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_short | Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_sort | algebraic properties of toeplitz operators on the pluriharmonic bergman space |
| url | http://dx.doi.org/10.1155/2013/578436 |
| work_keys_str_mv | AT jingyuyang algebraicpropertiesoftoeplitzoperatorsonthepluriharmonicbergmanspace AT liuliu algebraicpropertiesoftoeplitzoperatorsonthepluriharmonicbergmanspace AT yufenglu algebraicpropertiesoftoeplitzoperatorsonthepluriharmonicbergmanspace |