SPECTRAL DISSECTION OF FINITE RANK PERTURBATIONS OF NORMAL OPERATORS
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SPECTRAL DISSECTION OF FINITE RANK PERTURBATIONS OF NORMAL OPERATORS

  • Author(s): Putinar, Mihai
  • Yakubovich, Dmitry
  • et al.
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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