Algebraic Properties of Toeplitz Operators on the Polydisk
We discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydisk Dn. Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toe...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/962313 |
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| _version_ | 1832550181646630912 |
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| author | Bo Zhang Yanyue Shi Yufeng Lu |
| author_facet | Bo Zhang Yanyue Shi Yufeng Lu |
| author_sort | Bo Zhang |
| collection | DOAJ |
| description | We discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydisk Dn. Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toeplitz operators. Thirdly, we discuss finite rank semicommutators and commutators of Toeplitz operators with quasihomogeneous symbols. Finally, we solve the finite rank product problem for Toeplitz operators on the polydisk. |
| format | Article |
| id | doaj-art-016d71e3b4a24affb3fb0977293f9b86 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-016d71e3b4a24affb3fb0977293f9b862025-02-03T06:07:21ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/962313962313Algebraic Properties of Toeplitz Operators on the PolydiskBo Zhang0Yanyue Shi1Yufeng Lu2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Ocean University of China, Qingdao 266100, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaWe discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydisk Dn. Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toeplitz operators. Thirdly, we discuss finite rank semicommutators and commutators of Toeplitz operators with quasihomogeneous symbols. Finally, we solve the finite rank product problem for Toeplitz operators on the polydisk.http://dx.doi.org/10.1155/2011/962313 |
| spellingShingle | Bo Zhang Yanyue Shi Yufeng Lu Algebraic Properties of Toeplitz Operators on the Polydisk Abstract and Applied Analysis |
| title | Algebraic Properties of Toeplitz Operators on the Polydisk |
| title_full | Algebraic Properties of Toeplitz Operators on the Polydisk |
| title_fullStr | Algebraic Properties of Toeplitz Operators on the Polydisk |
| title_full_unstemmed | Algebraic Properties of Toeplitz Operators on the Polydisk |
| title_short | Algebraic Properties of Toeplitz Operators on the Polydisk |
| title_sort | algebraic properties of toeplitz operators on the polydisk |
| url | http://dx.doi.org/10.1155/2011/962313 |
| work_keys_str_mv | AT bozhang algebraicpropertiesoftoeplitzoperatorsonthepolydisk AT yanyueshi algebraicpropertiesoftoeplitzoperatorsonthepolydisk AT yufenglu algebraicpropertiesoftoeplitzoperatorsonthepolydisk |