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}
}
  • Aparajita Dasgupta, M. Ruzhansky
  • Published 2016
  • Mathematics
  • Journal d'Analyse Mathématique
  • 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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