Resolvents of operators inverse to Schatten–von Neumann ones

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Abstract

The paper deals with linear operators in a Hilbert space, whose inverse ones belong to the Schatten–von Neumann ideal of compact operators, and whose imaginary Hermitian components are bounded. A sharp norm estimate for the resolvents of the considered operators is derived. That estimate enables us to investigate spectrum perturbations and to establish bounds for the norms of the semigroups and Hirsch operator functions. The operator logarithm and fractional powers are examples of the Hirsch functions.

Original languageEnglish
Pages (from-to)363-376
Number of pages14
JournalAnnali dell'Universita di Ferrara
Volume60
Issue number2
DOIs
StatePublished - 1 Nov 2014

Keywords

  • Fractional powers
  • Hilbert space
  • Operator logarithm
  • Resolvent
  • Semigroup
  • Spectrum perturbations

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