Spectral dissection of finite rank perturbations of normal operators

2019/07/31 by Putinar, Mihai, Yakubovich, Dmitry
#30H10 #47A15 #47A45 #47A55 #47B20 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1907.13587

Abstract

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.

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