609 research outputs found
Relative residual bounds for eigenvalues in gaps of the essential spectrum
The relative distance between eigenvalues of the compression of a not
necessarily semibounded self-adjoint operator to a closed subspace and some of
the eigenvalues of the original operator in a gap of the essential spectrum is
considered. It is shown that this distance depends on the maximal angles
between pairs of associated subspaces. This generalises results by Drma\v{c} in
[Linear Algebra Appl. 244 (1996), 155--163] from matrices to not necessarily
(semi)bounded operators.Comment: 12 page
On a minimax principle in spectral gaps
The 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
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