Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators

Michael Gil’

doi:10.1080/00036811.2014.898271

Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators

Michael Gil’

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let (Formula presented.) be a Hilbert space with the unit operator (Formula presented.). The paper deals with the pencil (Formula presented.) , where (Formula presented.) and (Formula presented.) are Hilbert–Schmidt operators in (Formula presented.). We suggest a norm estimate for the inverse of (Formula presented.). By that estimate, bounds for the spectra of (Formula presented.) are established and perturbations by bounded operators are investigated. Applications to boundary value problems are also discussed.

Original language	English
Pages (from-to)	409-418
Number of pages	10
Journal	Applicable Analysis
Volume	94
Issue number	2
DOIs	https://doi.org/10.1080/00036811.2014.898271
State	Published - 1 Feb 2015

Keywords

inverse operator
linear operator pencil
spectrum

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/00036811.2014.898271

Cite this

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abstract = "Let (Formula presented.) be a Hilbert space with the unit operator (Formula presented.). The paper deals with the pencil (Formula presented.) , where (Formula presented.) and (Formula presented.) are Hilbert–Schmidt operators in (Formula presented.). We suggest a norm estimate for the inverse of (Formula presented.). By that estimate, bounds for the spectra of (Formula presented.) are established and perturbations by bounded operators are investigated. Applications to boundary value problems are also discussed.",

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AB - Let (Formula presented.) be a Hilbert space with the unit operator (Formula presented.). The paper deals with the pencil (Formula presented.) , where (Formula presented.) and (Formula presented.) are Hilbert–Schmidt operators in (Formula presented.). We suggest a norm estimate for the inverse of (Formula presented.). By that estimate, bounds for the spectra of (Formula presented.) are established and perturbations by bounded operators are investigated. Applications to boundary value problems are also discussed.

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KW - spectrum

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Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators

Abstract

Keywords

ASJC Scopus subject areas

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