Properties (BR) and (BgR) for bounded linear operators

Abstract

In this paper we introduce the notion of property (BR) and property (BgR) for bounded linear operators defined on an infinite-dimensional Banach space. These properties in connection with Weyl type theorems and in the frame of polaroid operators are investigated. Moreover, we study the stability of these properties under perturbations by commuting finite-dimensional, quasi-nilpotent, Riesz and algebraic operators.

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Acknowledgements

The authors are grateful to the referees for their valuable comments and suggestions. The corresponding author is supported by Department of Science and Technology, New Delhi, India (Grant No. DST/INSPIRE Fellowship/[IF170390]).

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Correspondence to Ankit Kumar.

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Gupta, A., Kumar, A. Properties (BR) and (BgR) for bounded linear operators. Rend. Circ. Mat. Palermo, II. Ser 69, 601–611 (2020). https://doi.org/10.1007/s12215-019-00422-3

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Keywords

  • Property (BR)
  • Property (BgR)
  • Weyl type theorems
  • SVEP
  • Polaroid operators
  • Perturbation theory

Mathematics Subject Classification

  • Primary 47A10
  • 47A11
  • Secondary 47A53
  • 47A55