Some lemmata on the perturbation of the spectrum

TL;DR

This paper provides conditions under which the second term in the spectral asymptotics of a compact operator remains stable when the metrics in the Hilbert space are perturbed.

Contribution

It introduces new sufficient conditions for spectral asymptotics stability under metric perturbations in Hilbert spaces.

Findings

Identifies conditions preserving the second spectral asymptotic term.

Provides theoretical criteria for spectral stability.

Enhances understanding of spectral perturbation effects.

Abstract

We give some sufficient conditions for preserving of the second term in the spectral asymptotics of a compact operator under the perturbation of the metrics in the Hilbert space.