A BOUND for SIMILARITY CONDITION NUMBERS of UNBOUNDED OPERATORS with HILBERT-SCHMIDT HERMITIAN COMPONENTS

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Abstract

Let H be a linear unbounded operator in a Hilbert space. It is assumed that the resolvent of H is a compact operator and H - H is a Hilbert-Schmidt operator. Various integro-differential operators satisfy these conditions. It is shown that H is similar to a normal operator and a sharp bound for the condition number is suggested. We also discuss applications of that bound to spectrum perturbations and operator functions.

Original languageEnglish
Pages (from-to)331-342
Number of pages12
JournalJournal of the Australian Mathematical Society
Volume97
Issue number3
DOIs
StatePublished - 20 Jun 2014

Keywords

  • condition numbers
  • norm of operator function
  • operators
  • similarity
  • spectrum perturbations

ASJC Scopus subject areas

  • Mathematics (all)

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