Continuity of the spectra for families of magnetic operators on Z^d

TL;DR

This paper proves that the spectral properties of magnetic operators on Z^d depend continuously on a parameter, using algebraic methods involving twisted crossed product C*-algebras.

Contribution

It establishes the continuity of spectral properties for families of magnetic operators on Z^d with respect to a parameter, employing an algebraic framework.

Findings

Spectral properties vary continuously with the parameter psilon.

Uses twisted crossed product C*-algebras for the proof.

Applicable to families of magnetic self-adjoint operators.

Abstract

For families of magnetic self-adjoint operators on ${\mathbb Z}^d$ whose symbols and magnetic fields depend continuously on a parameter $\epsilon$, it is shown that the main spectral properties of these operators also vary continuously with respect to $\epsilon$. The proof is based on an algebraic setting involving twisted crossed product C*-algebras.