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Journal of Function Spaces and Applications
Volume 2012, Article ID 789875, 13 pages
http://dx.doi.org/10.1155/2012/789875
Research Article

G-Convergence of Dirac Operators

Department of Mathematical Sciences, University of Gothenburg, 412 96 Gothenburg, Sweden

Received 2 November 2011; Revised 12 March 2012; Accepted 16 March 2012

Academic Editor: Bjorn Birnir

Copyright © 2012 Hasan Almanasreh and Nils Svanstedt. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.