Triple variational principles for self-adjoint operator functions

Matthias Langer, Michael Strauss

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5 Citations (Scopus)
36 Downloads (Pure)


For a very general class of unbounded self-adjoint operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find conditions which imply that a point is in the resolvent set. For norm resolvent continuous operator functions we show that the variational inequality becomes an equality.
Original languageEnglish
Pages (from-to)2019-2047
Number of pages29
JournalJournal of Functional Analysis
Issue number6
Early online date19 Jan 2016
Publication statusPublished - 15 Mar 2016


  • variational principles for eigenvalues
  • operator function
  • spectral decomposition


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