On Quasinormality of compact perturbations of the isometries
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914450038063104 |
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| author | Das, Susmita |
| author_facet | Das, Susmita |
| contents | We study the compact perturbations of an isometry on a separable Hilbert space and provide a complete characterization of when they are quasinormal. Based on that, we present a complete classification for a rank-one perturbation of a unilateral shift of finite multiplicity to be quasinormal in the setting of the Hardy space. The result can also be generalized for a separable Hilbert space. As an application, we provide a complete characterization for quasinormality of a rank-one perturbation of the Hardy shift. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_06967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Quasinormality of compact perturbations of the isometries Das, Susmita Functional Analysis 47A55, 47B20, 47B32, 47B38, 47B91 We study the compact perturbations of an isometry on a separable Hilbert space and provide a complete characterization of when they are quasinormal. Based on that, we present a complete classification for a rank-one perturbation of a unilateral shift of finite multiplicity to be quasinormal in the setting of the Hardy space. The result can also be generalized for a separable Hilbert space. As an application, we provide a complete characterization for quasinormality of a rank-one perturbation of the Hardy shift. |
| title | On Quasinormality of compact perturbations of the isometries |
| topic | Functional Analysis 47A55, 47B20, 47B32, 47B38, 47B91 |
| url | https://arxiv.org/abs/2512.06967 |