Absence of eigenvalues for the generalized two-dimensional periodic Dirac operator

Abstract

A generalized two-dimensional periodic Dirac operator is considered, with L ∞ - matrix-valued coefficients of the first order derivatives andwith complex matrix-valued poten- tial. It is proved that if the matrix-valued potential has zero bound relative to the free Dirac operator, then the spectrum of the operator in question contains no eigenvalues.