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Integral Equations and Operator Theory

, Volume 88, Issue 4, pp 559–599 | Cite as

Convergence of Sequences of Linear Operators and Their Spectra

  • Sabine Bögli
Article
  • 139 Downloads

Abstract

We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions that ensure spectral exactness, i.e. that every true eigenvalue is approximated and no spurious eigenvalues occur. A main ingredient is the discrete compactness of the sequence of resolvents of the approximating operators. We establish sufficient conditions and perturbation results for strong convergence and for discrete compactness of the resolvents.

Keywords

Eigenvalue approximation Spectral exactness Generalized resolvent convergence Discrete compactness 

Mathematics Subject Classification

47A10 47A55 47A58 47B07 

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Notes

Acknowledgements

The author would like to thank her doctoral advisor Christiane Tretter for the guidance. The work was supported by the Swiss National Science Foundation (SNF), Grant No. 200020_146477 and Early Postdoc.Mobility Project P2BEP2_159007.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMunichGermany

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