Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space
We study some algebraic properties of Toeplitz operator with quasihomogeneous or separately quasihomogeneous symbol on the pluriharmonic Bergman space of the unit ball in ℂn. We determine when the product of two Toeplitz operators with certain separately quasi-homogeneous symbols is a Toeplitz opera...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/252037 |
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| author | Hongyan Guan Liu Liu Yufeng Lu |
| author_facet | Hongyan Guan Liu Liu Yufeng Lu |
| author_sort | Hongyan Guan |
| collection | DOAJ |
| description | We study some algebraic properties of Toeplitz operator with quasihomogeneous or separately quasihomogeneous symbol on the pluriharmonic Bergman space of the unit ball in ℂn. We determine when the product of two Toeplitz operators with certain separately quasi-homogeneous symbols is a Toeplitz operator. Next, we discuss the zero-product problem for several Toeplitz operators, one of whose symbols is separately quasihomogeneous and the others are quasi-homogeneous functions, and show that the zero-product problem for two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary. Finally, we also characterize the commutativity of certain quasihomogeneous or separately quasihomogeneous Toeplitz operators. |
| format | Article |
| id | doaj-art-04ae6c3771444c89a1e89171a494c4c5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-04ae6c3771444c89a1e89171a494c4c52025-02-03T01:32:51ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/252037252037Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman SpaceHongyan Guan0Liu 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 operator with quasihomogeneous or separately quasihomogeneous symbol on the pluriharmonic Bergman space of the unit ball in ℂn. We determine when the product of two Toeplitz operators with certain separately quasi-homogeneous symbols is a Toeplitz operator. Next, we discuss the zero-product problem for several Toeplitz operators, one of whose symbols is separately quasihomogeneous and the others are quasi-homogeneous functions, and show that the zero-product problem for two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary. Finally, we also characterize the commutativity of certain quasihomogeneous or separately quasihomogeneous Toeplitz operators.http://dx.doi.org/10.1155/2013/252037 |
| spellingShingle | Hongyan Guan Liu Liu Yufeng Lu Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space Abstract and Applied Analysis |
| title | Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_full | Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_fullStr | Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_full_unstemmed | Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_short | Algebraic Properties of Quasihomogeneous and Separately Quasihomogeneous Toeplitz Operators on the Pluriharmonic Bergman Space |
| title_sort | algebraic properties of quasihomogeneous and separately quasihomogeneous toeplitz operators on the pluriharmonic bergman space |
| url | http://dx.doi.org/10.1155/2013/252037 |
| work_keys_str_mv | AT hongyanguan algebraicpropertiesofquasihomogeneousandseparatelyquasihomogeneoustoeplitzoperatorsonthepluriharmonicbergmanspace AT liuliu algebraicpropertiesofquasihomogeneousandseparatelyquasihomogeneoustoeplitzoperatorsonthepluriharmonicbergmanspace AT yufenglu algebraicpropertiesofquasihomogeneousandseparatelyquasihomogeneoustoeplitzoperatorsonthepluriharmonicbergmanspace |