On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator
Let g(z) be an n-degree polynomial (n≥2). Inspired by Sarason’s result, we introduce the operator T1 defined by the multiplication operator Mg plus the weighted Volterra operator Vg on the Bergman space. We show that the operator T1 is similar to Mg on some Hilbert space Sg2(D). Then for g(z)=zn, by...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/8370139 |
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| _version_ | 1832560925893197824 |
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| author | Yucheng Li Hao Chen Wenhua Lan |
| author_facet | Yucheng Li Hao Chen Wenhua Lan |
| author_sort | Yucheng Li |
| collection | DOAJ |
| description | Let g(z) be an n-degree polynomial (n≥2). Inspired by Sarason’s result, we introduce the operator T1 defined by the multiplication operator Mg plus the weighted Volterra operator Vg on the Bergman space. We show that the operator T1 is similar to Mg on some Hilbert space Sg2(D). Then for g(z)=zn, by using matrix manipulations, the reducing subspaces of the corresponding operator T2 on the Bergman space are characterized. |
| format | Article |
| id | doaj-art-182fc098d2f04c9d8a951ad9297104bb |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-182fc098d2f04c9d8a951ad9297104bb2025-02-03T01:26:18ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/83701398370139On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra OperatorYucheng Li0Hao Chen1Wenhua Lan2Department of Mathematics, Hebei Normal University, Hebei Province Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, ChinaDepartment of Mathematics, Hebei Normal University, Hebei Province Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, ChinaDepartment of Mathematics, Hebei Normal University, Hebei Province Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, ChinaLet g(z) be an n-degree polynomial (n≥2). Inspired by Sarason’s result, we introduce the operator T1 defined by the multiplication operator Mg plus the weighted Volterra operator Vg on the Bergman space. We show that the operator T1 is similar to Mg on some Hilbert space Sg2(D). Then for g(z)=zn, by using matrix manipulations, the reducing subspaces of the corresponding operator T2 on the Bergman space are characterized.http://dx.doi.org/10.1155/2017/8370139 |
| spellingShingle | Yucheng Li Hao Chen Wenhua Lan On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator Journal of Function Spaces |
| title | On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator |
| title_full | On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator |
| title_fullStr | On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator |
| title_full_unstemmed | On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator |
| title_short | On Similarity and Reducing Subspaces of the n-Shift plus Certain Weighted Volterra Operator |
| title_sort | on similarity and reducing subspaces of the n shift plus certain weighted volterra operator |
| url | http://dx.doi.org/10.1155/2017/8370139 |
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