Paired kernels and their applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917584715120640 |
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| author | Câmara, M. Cristina Partington, Jonathan R. |
| author_facet | Câmara, M. Cristina Partington, Jonathan R. |
| contents | This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Results on near-invariance properties, representations, and inclusion relations for these kernels are obtained. The existence of a minimal Toeplitz kernel containing any projected paired kernel and, more generally, any nearly $S^*$-invariant subspace of $H^2$, is derived. The results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16644 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Paired kernels and their applications Câmara, M. Cristina Partington, Jonathan R. Functional Analysis Complex Variables 30H10, 47B35, 47B38 This paper considers paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Results on near-invariance properties, representations, and inclusion relations for these kernels are obtained. The existence of a minimal Toeplitz kernel containing any projected paired kernel and, more generally, any nearly $S^*$-invariant subspace of $H^2$, is derived. The results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators. |
| title | Paired kernels and their applications |
| topic | Functional Analysis Complex Variables 30H10, 47B35, 47B38 |
| url | https://arxiv.org/abs/2308.16644 |