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

Dasgupta, A; Ruzhansky, M

doi:https://www.dx.doi.org/10.1007/s11854-016-0005-0

File(s)

10.1007%2Fs11854-016-0005-0.pdf (187.48 KB)

Published version

1306.0041v1.pdf (177.35 KB)

Accepted version

Author(s)

Dasgupta, A

Ruzhansky, M

Type

Journal Article

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.

Date Issued

2016-03-17

Date Acceptance

2013-07-29

Citation

Journal d'Analyse Mathematique, 2016, 128 (1), pp.179-190

URI

http://hdl.handle.net/10044/1/29778

DOI

https://www.dx.doi.org/10.1007/s11854-016-0005-0

ISSN

0021-7670

Publisher

Springer Verlag (Germany)

Start Page

179

End Page

190

Journal / Book Title

Journal d'Analyse Mathematique

Volume

128

Issue

1

Copyright Statement

Sponsor

Engineering & Physical Science Research Council (EPSRC)

Grant Number

EP/G007233/1

EP/K039407/1

Subjects

General Mathematics

0101 Pure Mathematics

Publication Status

Published