G-Convergence of Dirac Operators

Abstract EN

We consider the linear Dirac operator with a (−1)-homogeneous locally periodic potential that varies with respect to a small parameter.

Using the notation of G-convergence for positive self-adjoint operators in Hilbert spaces we prove G-compactness in the strong resolvent sense for families of projections of Dirac operators.

We also prove convergence of the corresponding point spectrum in the spectral gap.