Spectral dissection of finite rank perturbations of normal operators

Finite rank perturbations T = N + K of a bounded normal operator N on a separable Hilbert space are studied thanks to a natural functional model of T ; in its turn the functional model solely relies on a perturbation matrix/ characteristic function previously defined by the second author. Function t...

Descripción completa

Detalles Bibliográficos
Autores: Putinar, Mihai, Yakubóvich Lazarev, Dmitry
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/731780
Acceso en línea:https://hdl.handle.net/10486/731780
https://dx.doi.org/10.7900/jot.2019jul21.2266
Access Level:acceso embargado
Palabra clave:Bishop’s property (β)
decomposable operator
functional model
perturbation determinant
normal operator
Matemáticas
Descripción
Sumario:Finite rank perturbations T = N + K of a bounded normal operator N on a separable Hilbert space are studied thanks to a natural functional model of T ; in its turn the functional model solely relies on a perturbation matrix/ characteristic function previously defined by the second author. Function theoretic features of this perturbation matrix encode in a closed-form the spectral behavior of T . Under mild geometric conditions on the spectral measure of N and some smoothness constraints on K we show that the operator T admits invariant subspaces, or even it is decomposable