SPECTRAL DISSECTION OF FINITE RANK PERTURBATIONS OF NORMAL OPERATORS
- Author(s): Putinar, Mihai;
- Yakubovich, Dmitry
- et al.
Published Web Locationhttps://doi.org/10.7900/jot.2019jul21.2266
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.