On condition numbers of spectral operators in a hilbert space

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6 Scopus citations

Abstract

We consider a linear unbounded operator $$A$$A in a separable Hilbert space. with the following property: there is a normal operator $$D$$D with a discrete spectrum, such $$\Vert A-D\Vert <\infty $$‖A-D‖<∞. Besides, all the Eigen values of $$D$$D are different. Under certain assumptions it is shown that $$A$$A is similar to a normal operator and a sharp bound for the condition number is suggested. Applications of that bound to spectrum perturbations and operator functions are also discussed. As an illustrative example we consider a non-selfadjoint differential operator.

Original languageEnglish
Pages (from-to)363-372
Number of pages10
JournalAnalysis and Mathematical Physics
Volume5
Issue number4
DOIs
StatePublished - 1 Dec 2015

Keywords

  • Differential operator
  • Operator function
  • Similarity
  • Spectrum perturbations

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics

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