On similarity of unbounded perturbations of selfadjoint operators

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2 Scopus citations


We consider a linear unbounded operator A in a separable Hilbert space with the following property: there is an invertible selfadjoint operator S with a dis- crete spectrum such that ∥(A-S)S-v∥ <∞ for a v ε [0, 1]. Besides, all eigenvalues of S are assumed to be different. Under certain assumptions it is shown that A is si- milar 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)27-33
Number of pages7
JournalMethods of Functional Analysis and Topology
Issue number1
StatePublished - 1 Jan 2018


  • Operator function
  • Similarity
  • Spectrum perturbations
  • differential operator

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


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