On the Essential Spectrum of Operator Pencils

ABSTRACT For a closed densely defined linear operator A$A$ and a bounded linear operator B$B$ on a Banach space X$X$ whose essential spectrums are contained in disjoint sectors, we show that the essential spectrum of the associated operator pencil λA+B$\lambda A+ B$ is contained in a sector of the c...

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Bibliographic Details
Published inProceedings in applied mathematics and mechanics Vol. 24; no. 4
Main Authors Wilson, Mitsuru, Khelif, Hassen, Trunk, Carseten
Format Journal Article
LanguageEnglish
Published 01.12.2024
Online AccessGet full text
ISSN1617-7061
1617-7061
DOI10.1002/pamm.202400095

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Summary:ABSTRACT For a closed densely defined linear operator A$A$ and a bounded linear operator B$B$ on a Banach space X$X$ whose essential spectrums are contained in disjoint sectors, we show that the essential spectrum of the associated operator pencil λA+B$\lambda A+ B$ is contained in a sector of the complex plane whose boundaries are determined purely by the angles that define the two sectors, which contain the essential spectrums of A$A$ and B$B$.
ISSN:1617-7061
1617-7061
DOI:10.1002/pamm.202400095