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Journal of Spectral Theory

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Volume 8, Issue 4, 2018, pp. 1393–1442
DOI: 10.4171/JST/230

Published online: 2018-10-22

Spectral theory for structured perturbations of linear operators

Martin Adler[1] and Klaus-Jochen Engel[2]

(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