# The Gohberg Lemma, compactness, and essential spectrum of operators on compact Lie groups

@article{Dasgupta2016TheGL, title={The Gohberg Lemma, compactness, and essential spectrum of operators on compact Lie groups}, author={Aparajita Dasgupta and M. Ruzhansky}, journal={Journal d'Analyse Math{\'e}matique}, year={2016}, volume={128}, pages={179-190} }

We prove a version of the Gohberg Lemma on compact Lie groups giving an estimate from below for the distance from a given operator to the set of compact operators. As a consequence, we obtain several results on bounds for the essential spectrum and a criterion for an operator to be compact. The conditions are given in terms of the matrix-valued symbols of operators.

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