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Refinements of some inequalities involving Berezin norms and Berezin number and related questions

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Abstract

In this paper, we give several refinements of Berezin norm and Berezin number inequalities of bounded linear operators defined on a reproducing kernel Hilbert space. In particular, we present some refinements of the triangle inequality for the Berezin norm of operators. In addition, we derive new upper bounds for the sum and poduct of Berezin number for two bounded operators. Moreover, we prove some new upper bounds for the Davis–Wielandt–Berezin radius of operators. Some applications of the newly obtained inequalities are also provided.

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Funding

The first author was supported by the Researchers Supporting Project number RSP2023R1056, King Saud University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, B. Vagabzade st. 9, Baku, 370141, Azerbaijan

    Mubariz Garayev

  2. Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia

    Mubariz Garayev

  3. Faculty of Exact Sciences, Department of Mathematics, El Oued University, 39000, El Oued, Algeria

    Messaoud Guesba

Authors
  1. Mubariz Garayev
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  2. Messaoud Guesba
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Correspondence to Messaoud Guesba.

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Garayev, M., Guesba, M. Refinements of some inequalities involving Berezin norms and Berezin number and related questions. Ann Univ Ferrara (2023). https://doi.org/10.1007/s11565-023-00477-2

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