Gohberg lemma, compactness, and essential spectrum of operators on compact Lie groups
arXiv:1306.0041 · doi:10.1007/s11854-016-0005-0
Abstract
In this paper 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 on compact Lie groups. As a consequence, we prove 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.
13 pages