Toeplitz Operators on the Dirichlet Space of 𝔹n
We study the algebraic properties of Toeplitz operators on the Dirichlet space of the unit ball 𝔹n. We characterize pluriharmonic symbol for which the corresponding Toeplitz operator is normal or isometric. We also obtain descriptions of conjugate holomorphic symbols of commuting Toeplitz operators....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/958201 |
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| _version_ | 1832549876830830592 |
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| author | HongZhao Lin YuFeng Lu |
| author_facet | HongZhao Lin YuFeng Lu |
| author_sort | HongZhao Lin |
| collection | DOAJ |
| description | We study the algebraic properties of Toeplitz operators on the Dirichlet
space of the unit ball 𝔹n. We characterize pluriharmonic symbol for which the corresponding
Toeplitz operator is normal or isometric. We also obtain descriptions of conjugate holomorphic
symbols of commuting Toeplitz operators. Finally, the commuting problem of Toeplitz operators
whose symbols are of the form zpz¯qϕ(|z|2) is studied. |
| format | Article |
| id | doaj-art-ad853e153bac457b93381ac24499c43f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ad853e153bac457b93381ac24499c43f2025-02-03T06:08:28ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/958201958201Toeplitz Operators on the Dirichlet Space of 𝔹nHongZhao Lin0YuFeng Lu1School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, ChinaWe study the algebraic properties of Toeplitz operators on the Dirichlet space of the unit ball 𝔹n. We characterize pluriharmonic symbol for which the corresponding Toeplitz operator is normal or isometric. We also obtain descriptions of conjugate holomorphic symbols of commuting Toeplitz operators. Finally, the commuting problem of Toeplitz operators whose symbols are of the form zpz¯qϕ(|z|2) is studied.http://dx.doi.org/10.1155/2012/958201 |
| spellingShingle | HongZhao Lin YuFeng Lu Toeplitz Operators on the Dirichlet Space of 𝔹n Abstract and Applied Analysis |
| title | Toeplitz Operators on the Dirichlet Space of 𝔹n |
| title_full | Toeplitz Operators on the Dirichlet Space of 𝔹n |
| title_fullStr | Toeplitz Operators on the Dirichlet Space of 𝔹n |
| title_full_unstemmed | Toeplitz Operators on the Dirichlet Space of 𝔹n |
| title_short | Toeplitz Operators on the Dirichlet Space of 𝔹n |
| title_sort | toeplitz operators on the dirichlet space of 𝔹n |
| url | http://dx.doi.org/10.1155/2012/958201 |
| work_keys_str_mv | AT hongzhaolin toeplitzoperatorsonthedirichletspaceofbn AT yufenglu toeplitzoperatorsonthedirichletspaceofbn |