Journal of Operator Theory

Volume 59, Issue 1, Winter 2008 pp. 115-155.

Compact perturbations and stability of the essential spectrum of singular differential operators

Authors: V. Georgescu (1) and S. Golenia (2)
Author institution:(1) Departement de Mathematiques, Universite de Cergy-Pontoise, 95302 Cergy-Pontoise, France
(2) Departement de Mathematiques, Universite de Cergy-Pontoise, 95302 Cergy-Pontoise, France

Summary: We establish criteria which ensure that the difference of the resolvents of two unbounded operators acting in Banach modules is compact. The applications cover operators acting on sections of vector fiber bundles over non-smooth manifolds or locally compact abelian groups, in particular differential operators of any order with complex measurable coefficients on $\R^n$, singular Dirac operators, and Laplace-Beltrami operators on Riemannian manifolds with measurable metrics.

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