Hyperinvariant subspaces for trace class perturbations of normal operators and decomposability
Functional Analysis
2025-03-03 v1
Abstract
We prove that a large class of trace-class perturbations of diagonalizable normal operators on a separable, infinite dimensional complex Hilbert space have non-trivial closed hyperinvariant subspaces. Moreover, a large subclass consists of decomposable operators in the sense of Colojoar\u{a} and Foia\c{s}.
Cite
@article{arxiv.2502.20912,
title = {Hyperinvariant subspaces for trace class perturbations of normal operators and decomposability},
author = {Eva A. Gallardo-Gutiérrez and F. Javier González-Doña},
journal= {arXiv preprint arXiv:2502.20912},
year = {2025}
}
Comments
Accepted for publication in Journal of Functional Analysis