Paired kernels and their applications
| Autor: | Câmara, M. Cristina, Partington, Jonathan R. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 26 pages; some minor corrections |
| Databáze: | arXiv |
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