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Zeitschrift für Analysis und ihre Anwendungen

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Volume 18, Issue 4, 1999, pp. 859–873
DOI: 10.4171/ZAA/919

Published online: 1999-12-31

On the Spectrum of Orthomorphisms and Barbashin Operators

E.A. Biberdorf[1] and Martin Väth[2]

(1) Universität Würzburg, Germany
(2) Czech Academy of Sciences, Prague, Czech Republic

The paper is concerned with the spectrum of an operator $A = C + K$, where $C$ is an orthomorphism and $K$ is a compact operator. The proofs are in a certain sense constructive. The results are applied to Barbashin equations $\frac{dx}{dt} = Ax$, where $A = C+K$ with a multiplication operator $C$ and an integral operator $K$. In some particular cases even necessary and sufficient conditions for stability are given.

Keywords: Barbashin equations, orthomorphisms in Bonach lattices, essential spectrum, spectral estimates, perturbations

Biberdorf E.A., Väth Martin: On the Spectrum of Orthomorphisms and Barbashin Operators. Z. Anal. Anwend. 18 (1999), 859-873. doi: 10.4171/ZAA/919