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

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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.

Original languageEnglish
Pages (from-to)409-418
Number of pages10
JournalApplicable Analysis
Volume94
Issue number2
DOIs
StatePublished - 1 Feb 2015

Keywords

  • inverse operator
  • linear operator pencil
  • spectrum

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