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

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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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Chicago
Dasgupta, Aparajita, and Michael Ruzhansky. 2016. “The Gohberg Lemma, Compactness, and Essential Spectrum of Operators on Compact Lie Groups.” Journal D Analyse Mathematique 128: 179–190.
APA
Dasgupta, A., & Ruzhansky, M. (2016). The Gohberg Lemma, compactness, and essential spectrum of operators on compact Lie groups. JOURNAL D ANALYSE MATHEMATIQUE , 128, 179–190.
Vancouver
1.
Dasgupta A, Ruzhansky M. The Gohberg Lemma, compactness, and essential spectrum of operators on compact Lie groups. JOURNAL D ANALYSE MATHEMATIQUE . 2016;128:179–90.
MLA
Dasgupta, Aparajita, and Michael Ruzhansky. “The Gohberg Lemma, Compactness, and Essential Spectrum of Operators on Compact Lie Groups.” JOURNAL D ANALYSE MATHEMATIQUE 128 (2016): 179–190. Print.
@article{8585366,
  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.},
  author       = {Dasgupta, Aparajita and Ruzhansky, Michael},
  issn         = {0021-7670},
  journal      = {JOURNAL D ANALYSE MATHEMATIQUE },
  language     = {eng},
  pages        = {179--190},
  title        = {The Gohberg Lemma, compactness, and essential spectrum of operators on compact Lie groups},
  url          = {http://dx.doi.org/10.1007/s11854-016-0005-0},
  volume       = {128},
  year         = {2016},
}

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