On a minimax principle in spectral gaps
Spectral Theory
2022-03-04 v3 Mathematical Physics
Functional Analysis
math.MP
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.
Cite
@article{arxiv.2008.02489,
title = {On a minimax principle in spectral gaps},
author = {Albrecht Seelmann},
journal= {arXiv preprint arXiv:2008.02489},
year = {2022}
}
Comments
31 pages; modified introduction, added references and appendix, some editorial changes and fixed typos