Gallardo Gutiérrez, Eva AntoniaGonzález Doña, F. Javier2023-09-052023-09-052023-08-3010.1016/j.jfa.2023.110148https://hdl.handle.net/20.500.14352/87560We 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1016/j.jfa.2023.110148open access51Finite rank perturbations of normal operatorsInvariant subspacesSpectral subspacesDecomposable operatorsMatemáticas (Matemáticas)12 Matemáticas