On the continuity of spectra for families of magnetic pseudodifferential operators

TL;DR

This paper proves that the spectra of families of magnetic pseudodifferential operators change continuously as the underlying symbols and magnetic fields vary with a real parameter.

Contribution

It establishes the spectral continuity for parameter-dependent magnetic pseudodifferential operators, extending previous results to this specific class.

Findings

Spectra vary continuously with the parameter.

Continuity holds under the dependence of symbols and magnetic fields.

Provides a rigorous mathematical framework for spectral stability.

Abstract

For families of magnetic pseudodifferential operators defined by symbols and magnetic fields depending continuously on a real parameter $\epsilon$, we show that the corresponding family of spectra also varies continuously with $\epsilon$.