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A new approach to numerical radius of quadratic operators

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Abstract

In this paper, we give an elementary approach to the numerical radius and norms of the real and imaginary parts of a quadratic operator in terms of its norm. This method is based on proving equality of the numerical radius with one of its suitable upper bounds, via successively establishing equality of the numerical radius with some of its intermediate upper bounds. Meanwhile, some other related results are obtained.

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Acknowledgements

The authors would like to thank the anonymous referee for the helpful comments and useful suggestions to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, 45137-66731, Iran

    Jamal Rooin, Saeed Karami & Masoomeh Ghaderi Aghideh

Authors
  1. Jamal Rooin
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  2. Saeed Karami
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  3. Masoomeh Ghaderi Aghideh
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Correspondence to Saeed Karami.

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Communicated by Marek Ptak.

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Rooin, J., Karami, S. & Ghaderi Aghideh, M. A new approach to numerical radius of quadratic operators. Ann. Funct. Anal. 11, 879–896 (2020). https://doi.org/10.1007/s43034-020-00072-y

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  • DOI: https://doi.org/10.1007/s43034-020-00072-y

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