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Generalized numerical radius of a bounded linear operator

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Abstract

In this paper, we considered the generalized numerical radius of a bounded linear operator defined from a Hilbert space H into itself and derived certain basic properties of generalized numerical radius of normal and hyponormal operators. We then concentrate on nilpotent operators and operators that are involutions and idempotents and present estimates for the generalized numerical radius. We also considered several examples to illustrate our results.

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Acknowledgements

The authors thank the referee and the editor for the valuable suggestions and comments on an earlier version. Incorporating appropriate responses to these in the article has led to a better presentation of the results.

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Authors and Affiliations

  1. P.G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, 751004, India

    Namita Das & Mamata Rani Jena

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  1. Namita Das
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  2. Mamata Rani Jena
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Correspondence to Mamata Rani Jena.

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Communicated by Yiu-Tung Poon.

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Das, N., Jena, M.R. Generalized numerical radius of a bounded linear operator. Adv. Oper. Theory 8, 62 (2023). https://doi.org/10.1007/s43036-023-00289-3

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