Almost invariant subspaces of shift operators and products of Toeplitz and Hankel operators
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915027389251584 |
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| author | Gu, Caixing Hwang, In Sung Kim, Hyoung Joon Lee, Woo Young Park, Jaehui |
| author_facet | Gu, Caixing Hwang, In Sung Kim, Hyoung Joon Lee, Woo Young Park, Jaehui |
| contents | In this paper we formulate the almost invariant subspaces theorems of backward shift operators in terms of the ranges or kernels of product of Toeplitz and Hankel operators. This approach simplifies and gives more explicit forms of these almost invariant subspaces which are derived from related nearly backward shift invariant subspaces with finite defect. Furthermore, this approach also leads to the surprising result that the almost invariant subspaces of backward shift operators are the same as the almost invariant subspaces of forward shift operators which were treated only briefly in literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_13177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost invariant subspaces of shift operators and products of Toeplitz and Hankel operators Gu, Caixing Hwang, In Sung Kim, Hyoung Joon Lee, Woo Young Park, Jaehui Functional Analysis 47A15, 47B35, 47B38 In this paper we formulate the almost invariant subspaces theorems of backward shift operators in terms of the ranges or kernels of product of Toeplitz and Hankel operators. This approach simplifies and gives more explicit forms of these almost invariant subspaces which are derived from related nearly backward shift invariant subspaces with finite defect. Furthermore, this approach also leads to the surprising result that the almost invariant subspaces of backward shift operators are the same as the almost invariant subspaces of forward shift operators which were treated only briefly in literature. |
| title | Almost invariant subspaces of shift operators and products of Toeplitz and Hankel operators |
| topic | Functional Analysis 47A15, 47B35, 47B38 |
| url | https://arxiv.org/abs/2411.13177 |