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Polynomially normal operators

  • Dragan S. Djordjević
  • Muneo Chō
  • Dijana MosićEmail author
Original Paper

Abstract

In this paper, we introduce a polynomially normal operator on a complex Hilbert space, extending the notation of n-normal and normal operators. Several basic properties of polynomially normal operator are firstly presented. We show some spectral properties of polynomially normal operators under new assumption in literature. Precisely, we prove that \(\sigma (T)=\sigma _a(T)\), \(\ker (T-z) \, \bot \, \ker (T - w)\) if z and w are distinct eigen-values of T and others results. Thus, we generalize some results for n-normal and normal operators.

Keywords

Hilbert space Linear operator Normal operator Spectrum SVEP 

Mathematics Subject Classification

47B15 47A15 

Notes

Acknowledgements

This research is supported by the Ministry of Science, Republic of Serbia, Grant no. 174007. This is partially supported by Grant-in-Aid Scientific Research No.15K04910.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  • Dragan S. Djordjević
    • 1
  • Muneo Chō
    • 2
  • Dijana Mosić
    • 1
    Email author
  1. 1.Faculty of Sciences and MathematicsUniversity of NišNišSerbia
  2. 2.Department of MathematicsKanagawa UniversityHiratsukaJapan

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