AN UNBOUNDED OPERATOR WITH SPECTRUM IN A STRIP AND MATRIX DIFFERENTIAL OPERATORS

Michael Gil'

Research output: Contribution to journalArticlepeer-review

Abstract

Let A and à be unbounded linear operators on a Hilbert space. We consider the following problem. Let the spectrum of A lie in some horizontal strip. In which strip does the spectrum of à lie, if A and à are sufficiently 'close'? We derive a sharp bound for the strip containing the spectrum of Ã, assuming that à - A is a bounded operator and A has a bounded Hermitian component. We also discuss applications of our results to regular matrix differential operators.

Original languageEnglish
Pages (from-to)146-153
Number of pages8
JournalBulletin of the Australian Mathematical Society
Volume105
Issue number1
DOIs
StatePublished - 16 Feb 2022
Externally publishedYes

Keywords

  • Differential operator
  • Hilbert space
  • Spectrum localisation

ASJC Scopus subject areas

  • Mathematics (all)

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