Seelmann, Albrecht2023-04-252023-04-252022-03-03http://hdl.handle.net/2003/41351http://dx.doi.org/10.17877/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.enMinimax valuesEigenvalues in gap of the essential spectrumBlock diagonalizationStokes operator510Text