Finite rank perturbations of normal operators: spectral idempotents and decomposability
We prove that a large class of finite rank perturbations of diagonal operators and, in general, of diagonalizable normal operators of multiplicity one acting boundedly on a separable, infinite dimensional complex Hilbert space are decomposable operators in the sense of Colojoară and Foiaş [1]. Conse...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/87560 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/87560 |
| Access Level: | acceso abierto |
| Palabra clave: | 51 Finite rank perturbations of normal operators Invariant subspaces Spectral subspaces Decomposable operators Matemáticas (Matemáticas) 12 Matemáticas |
| Sumario: | We prove that a large class of finite rank perturbations of diagonal operators and, in general, of diagonalizable normal operators of multiplicity one acting boundedly on a separable, infinite dimensional complex Hilbert space are decomposable operators in the sense of Colojoară and Foiaş [1]. Consequently, every operator T in such a class has a rich spectral structure and plenty of non-trivial closed hyperinvariant subspaces which extends, in particular, previous theorems of Foiaş, Jung, Ko and Pearcy [5], [6], [7], Fang and J. Xia [3] and the authors [8], [9] on an open question posed by Pearcy in the seventies. |
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