On a minimax principle in spectral gaps

Abstract

The minimax principle for eigenvalues in gaps of the essential spectrum in the form presented by Griesemer, Lewis, and Siedentop in [Doc. Math. 4 (1999), 275--283] is adapted to cover certain abstract perturbative settings with bounded or unbounded perturbations, in particular ones that are off-diagonal with respect to the spectral gap under consideration. This in part builds upon and extends the considerations in the author's appendix to [J. Spectr. Theory 10 (2020), 843--885]. Several monotonicity and continuity properties of eigenvalues in gaps of the essential spectrum are deduced, and the Stokes operator is revisited as an example.

31 pages; modified introduction, added references and appendix, some editorial changes and fixed typos

References in corpus (3)

• On the eigenvalues of operators with gaps. Application to Dirac operators
• Spectral perturbation bounds for selfadjoint operators
• Unifying the treatment of indefinite and semidefinite perturbations in the subspace perturbation problem