We consider a general framework for investigating spectral pollution in the Galerkin method. We show how this phenomenon is characterised via the existence of particular Weyl sequences which are singular in a suitable sense. For a given semi-bounded selfadjoint operator A, we identify relative compactness conditions on a selfadjoint perturbation B, ensuring that the limiting set of spectral pollution of A and B coincide. Our results show that, under perturbation, this limiting set behaves in a similar fashion as the essential spectrum.
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Lyonell Boulton, Nabile Boussaïd, Mathieu Lewin, Generalized Weyl theorems and spectral pollution in the Galerkin method. J. Spectr. Theory 2 (2012), no. 4, pp. 329–354DOI 10.4171/JST/32