Abstract
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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The first author was supported by the Grace-Chisholm Young Fellowship of the London Mathematical Society.
The second author was supported by the EPSRC Leadership Fellowship EP/G007233/1 and by EPSRC Grant EP/K039407/1. No new data was collected or generated during the course of the research.
An erratum to this article is available at http://dx.doi.org/10.1007/s11854-017-0024-5.
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Dasgupta, A., Ruzhansky, M. The Gohberg Lemma, compactness, and essential spectrum of operators on compact Lie groups. JAMA 128, 179–190 (2016). https://doi.org/10.1007/s11854-016-0005-0
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DOI: https://doi.org/10.1007/s11854-016-0005-0