Norm estimates for functions of non-selfadjoint operators nonregular on the convex hull of the spectrum

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Abstract

We consider a bounded linear operator A in a Hilbert space with a Hilbert-Schmidt Hermitian component (A A*)/2i. A sharp norm estimate is established for functions of A nonregular on the convex hull of the spectrum. The logarithm, fractional powers and meromorphic functions of operators are examples of such functions. Our results are based on the existence of a sequence An (n = 1, 2, ...) of nite dimensional operators strongly converging to A, whose spectra belongs to the spectrum of A. Besides, it is shown that the resolvents and holomorphic functions of An strongly converge to the resolvent and corresponding function of A.

Original languageEnglish
Pages (from-to)267-277
Number of pages11
JournalDemonstratio Mathematica
Volume50
Issue number1
DOIs
StatePublished - 1 Mar 2017

Keywords

  • Fractional power
  • Functions of non-selfadjoint operators
  • Logarithm
  • Meromorphic function

ASJC Scopus subject areas

  • General Mathematics

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