EMIS ELibM Electronic Journals Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 4, pp. 859-873 (1999)

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On the Spectrum of Orthomorphisms and Barbashin Operators

E. A. Biberdorf and M. Väth

Both authors: Univ. of Würzburg, Dept. Math., Am Hubland, D-97074 Würzburg; Current address of E. A. Biberdorf: Zolotodolinskaja ul. 21-45, 630090 Novosibirsk, Russia; ermolova@math.nsc.ru \ and \ vaeth@cip.mathematik.uni-wuerzburg.de

Abstract: 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 ${dx \over dt} = Ax$, 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 Banach lattices, essential spectrum, spectral estimates, perturbations

Classification (MSC2000): 45K05, 47B38, 47B65

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Electronic fulltext finalized on: 7 Aug 2001. This page was last modified: 9 Nov 2001.

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