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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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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DOI: https://doi.org/10.1007/s12215-019-00422-3