Inner and outer continuity of the spectra for families of magnetic operators on $mathbb{Z}^{d}$ (Spectral and Scattering Theory and Related Topics)

Abstract

In this note we consider magnetic self-adjoint operators on mathbb{Z}^{d} whose symbols and magnetic fields depend on a parameter $epsilon$. Sufficient conditions are imposed such that the spectrum of these operators varies continuously with respect to $epsilon$. The emphasize is put on a construction which is independent of any particular choice of the magnetic potentials.