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

2013/05/31 by Aparajita Dasgupta, Michael Ruzhansky
Mathematics · #Advanced Harmonic Analysis Research #Algebra over a field #Essential spectrum #Holomorphic and Operator Theory #Lemma (botany) #Lie group #Mathematical Analysis and Transform Methods #Operator (biology) #Set (abstract data type) #Spectrum (functional analysis) #math.FA #math.SP #msc:22C05 #msc:43A77 #msc:47A53 #msc:47G30

paper · pdf · doi:10.1007/s11854-016-0005-0

published as J. Anal. Math., 128 (2016), 179-190 · 13 pages

arxiv created 2013/05/31 · openalex publication_date 2016/02/01 · arxiv updated 2016/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Global Quantization of Pseudo-Differential Operators on Compact Lie Groups, SU(2), 3-sphere, and Homogeneous Spaces