Journal of Spectral Theory
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Published online: 2018-10-22
Spectral theory for structured perturbations of linear operatorsMartin Adler and Klaus-Jochen Engel (1) Universität Tübingen, Germany
(2) Università degli Studi dell’Aquila, Italy
We characterize the spectrum (and its parts) of operators which can be represented as "$G=A+BC“$ for a "simpler" operator $A$ and a structured perturbation $BC$. The interest in this kind of perturbations is motivated, e.g., by perturbations of the domain of an operator $A$ but also arises in the theory of closed-loop systems in control theory. In many cases our results yield the spectral values of $G$ as zeros of a "characteristic equation".
Keywords: Spectrum, linear operator, structured perturbation, resolvent
Adler Martin, Engel Klaus-Jochen: Spectral theory for structured perturbations of linear operators. J. Spectr. Theory 8 (2018), 1393-1442. doi: 10.4171/JST/230