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Generalized Upper Bounds Estimation of Numerical Radius and Norm for the Sum of Operators

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Abstract

We give some generalized upper bounds for the numerical radius and usual operator norm of the sum of two Hilbert space operators. These inequalities are mainly based on the extension Buzano inequality and the generalized Young inequality. And our bounds refine and generalize the existing related upper bounds.

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Acknowledgements

The authors are very grateful to the anonymous referees for their valuable suggestions and comments which have greatly improved this paper.

Funding

This work is supported by the NNSF of China (Grant Nos. 11561048, 11761029), and the NSF of Inner Mongolia (Grant Nos. 2019MS01019, 2020ZD01).

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Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, People’s Republic of China

    Muqile Gao & Deyu Wu

  2. Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China

    Alatancang Chen

Authors
  1. Muqile Gao
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  2. Deyu Wu
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  3. Alatancang Chen
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Contributions

MG wrote the main manuscript text. DW and AC are primarily responsible for proposing concepts, revising manuscripts and securing funding.

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Correspondence to Deyu Wu.

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Gao, M., Wu, D. & Chen, A. Generalized Upper Bounds Estimation of Numerical Radius and Norm for the Sum of Operators. Mediterr. J. Math. 20, 210 (2023). https://doi.org/10.1007/s00009-023-02405-2

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  • DOI: https://doi.org/10.1007/s00009-023-02405-2

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