Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk
We consider the reducing subspaces of MzN on Aα2(Dk), where k≥3, zN=z1N1⋯zkNk, and Ni≠Nj for i≠j. We prove that each reducing subspace of MzN is a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases that α=0 and α∈(-1,+∞)∖Q, respectively. F...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/209307 |
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| _version_ | 1832562479569305600 |
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| author | Yanyue Shi Na Zhou |
| author_facet | Yanyue Shi Na Zhou |
| author_sort | Yanyue Shi |
| collection | DOAJ |
| description | We consider the reducing subspaces of MzN on Aα2(Dk), where k≥3, zN=z1N1⋯zkNk, and Ni≠Nj for i≠j. We prove that each reducing subspace of MzN is a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases that α=0 and α∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces of MzN on Aα2(D3) with α>-1. |
| format | Article |
| id | doaj-art-88000bc1cb91474383e10509b70a3527 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-88000bc1cb91474383e10509b70a35272025-02-03T01:22:31ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/209307209307Reducing Subspaces of Some Multiplication Operators on the Bergman Space over PolydiskYanyue Shi0Na Zhou1School of Mathematical Sciences, Ocean University of China, Qingdao 266000, ChinaSchool of Mathematical Sciences, Ocean University of China, Qingdao 266000, ChinaWe consider the reducing subspaces of MzN on Aα2(Dk), where k≥3, zN=z1N1⋯zkNk, and Ni≠Nj for i≠j. We prove that each reducing subspace of MzN is a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases that α=0 and α∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces of MzN on Aα2(D3) with α>-1.http://dx.doi.org/10.1155/2015/209307 |
| spellingShingle | Yanyue Shi Na Zhou Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk Abstract and Applied Analysis |
| title | Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk |
| title_full | Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk |
| title_fullStr | Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk |
| title_full_unstemmed | Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk |
| title_short | Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk |
| title_sort | reducing subspaces of some multiplication operators on the bergman space over polydisk |
| url | http://dx.doi.org/10.1155/2015/209307 |
| work_keys_str_mv | AT yanyueshi reducingsubspacesofsomemultiplicationoperatorsonthebergmanspaceoverpolydisk AT nazhou reducingsubspacesofsomemultiplicationoperatorsonthebergmanspaceoverpolydisk |