Polynomially normal operators

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.

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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.

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Correspondence to Dijana Mosić.

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The authors declare that they have no conflict of interest.

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Communicated by Hugo Woerdeman.

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Djordjević, D.S., Chō, M. & Mosić, D. Polynomially normal operators. Ann. Funct. Anal. 11, 493–504 (2020). https://doi.org/10.1007/s43034-019-00033-0

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Keywords

  • Hilbert space
  • Linear operator
  • Normal operator
  • Spectrum
  • SVEP

Mathematics Subject Classification

  • 47B15
  • 47A15