We establish some 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 R, singular Dirac operators and Laplace-Beltrami ...

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The paper is devoted to local derivations on the algebra S(M, τ) of τ measurable operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every local derivation on S(M, τ) which is continuous in the measure topology, is in fact a derivation. In the particular case of type I von Neumann algebras they all are inner derivations. It is proved that f...