Integral Equations and Operator Theory

, Volume 28, Issue 1, pp 72–86 | Cite as

On the approximation of positive operators and the behaviour of the spectra of the approximants

  • Frank Räbiger
  • Manfred P. H. Wolff
Article

Abstract

LetT be a positive linear operator on the Banach latticeE and let (Sn) be a sequence of bounded linear operators onE which converge strongly toT. Our main results are concerned with the question under which additional assumptions onSn andT the peripheral spectra πσ(Sn) ofSn converge to the peripheral spectrum πσ(T) ofT. We are able to treat even the more general case of discretely convergent sequences of operators.

1991 Mathematics Subject Classification

47A58 47B65 47A10 

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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Frank Räbiger
    • 1
  • Manfred P. H. Wolff
    • 1
  1. 1.Mathematisches InstitutUniversität TübingenTübingenGermany

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