Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 4, pp. 859873 (1999) 

On the Spectrum of Orthomorphisms and Barbashin OperatorsE. A. Biberdorf and M. VäthBoth authors: Univ. of Würzburg, Dept. Math., Am Hubland, D97074 Würzburg; Current address of E. A. Biberdorf: Zolotodolinskaja ul. 2145, 630090 Novosibirsk, Russia; ermolova@math.nsc.ru \ and \ vaeth@cip.mathematik.uniwuerzburg.deAbstract: 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 Full text of the article:
Electronic fulltext finalized on: 7 Aug 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
