Continuity of the spectra for families of magnetic operators on Z^d
arXiv:1509.04894 · doi:10.1007/s13324-015-0121-5
Abstract
For families of magnetic self-adjoint operators on ${\mathbb Z}^d$ whose symbols and magnetic fields depend continuously on a parameter $ε$, it is shown that the main spectral properties of these operators also vary continuously with respect to $ε$. The proof is based on an algebraic setting involving twisted crossed product C*-algebras.
13 pages