Seelmann, Albrecht2023-04-252023-04-252022-03-03http://hdl.handle.net/2003/4135110.17877/DE290R-23194The minimax principle for eigenvalues in gaps of the essential spectrum in the form presented by Griesemer et al. (Doc Math 4:275–283, 1999) 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 Nakić et al. (J Spectr Theory 10:843–885, 2020). Several monotonicity and continuity properties of eigenvalues in gaps of the essential spectrum are deduced, and the Stokes operator is revisited as an example.enComplex analysis and operator theory;16(3)https://creativecommons.org/licenses/by/4.0/Minimax valuesEigenvalues in gap of the essential spectrumBlock diagonalizationStokes operator510article (journal)