Decay Preserving Operators and Stability of the Essential Spectrum

Abstract

We establish criteria for the stability of the essential spectrum for unbounded operators acting in Banach modules. 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 an euclidean space, singular Dirac operators, and Laplace-Beltrami operators on Riemannian manifolds with measurable metrics.

This revised version differs from the original one in three respects: 1. Several improvements of the stability criteria for operators in divergence form on an Euclidean space and for Laplace operators on Riemannian manifolds. 2. New references and comments clarify the class of manifolds to which our abstract results can be applied. 2. A rather important reorganization of the paper should make it more readable

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• The spectrum of magnetic Schrödinger operators and $k$-form Laplacians on conformally cusp manifolds
• Trace estimates and invariance of the essential spectrum