JournalszaaVol. 18, No. 4pp. 859–873

On the Spectrum of Orthomorphisms and Barbashin Operators

  • E.A. Biberdorf

    Universität Würzburg, Germany
  • Martin Väth

    Czech Academy of Sciences, Prague, Czech Republic
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Abstract

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

Cite this article

E.A. Biberdorf, Martin Väth, On the Spectrum of Orthomorphisms and Barbashin Operators. Z. Anal. Anwend. 18 (1999), no. 4, pp. 859–873

DOI 10.4171/ZAA/919