The Gohberg Lemma, compactness, and essential spectrum of operators on compact Lie groups
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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.
KeywordsCompact Operator Fredholm Operator Complex Banach Space Matrix Quantization Matrix Symbol
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