Inner bounds for the spectrum of quasinormal operators

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Abstract

A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.

Original languageEnglish
Pages (from-to)3737-3746
Number of pages10
JournalProceedings of the American Mathematical Society
Volume131
Issue number12
DOIs
StatePublished - 1 Dec 2003

Keywords

  • Finite and infinite matrices
  • Integral operators
  • Linear operators
  • Spectral radius
  • Spectrum

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