Eigenvalues in gaps of selfadjoint operators in Pontryagin spaces

TL;DR

This paper investigates the eigenvalue differences of selfadjoint operators in Pontryagin spaces, establishing bounds based on resolvent differences and space index, contributing to spectral theory in indefinite inner product spaces.

Contribution

It provides a new bound on the difference of eigenvalue multiplicities for selfadjoint operators in Pontryagin spaces with finite resolvent difference.

Findings

Eigenvalue multiplicity difference is bounded by n+2κ.

Results apply to operators with n-dimensional resolvent difference.

Advances spectral analysis in indefinite inner product spaces.

Abstract

Given an open real interval \Delta\ and two selfadjoint operators A_1, A_2 in a \Pi_\kappa-space with n-dimensional resolvent difference we show that the difference of the total multiplicities of the eigenvalues of A_1 and A_2 in \Delta\ is at most n+2\kappa.