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Some inequalities involving Berezin symbols of operator means and related questions

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, by using some classical operator means and classical operator inequalities, we investigate Berezin number of operators. In particular, we compare the Berezin number of some operator means of two positive operators. We also use some Hardy type inequalities to obtain a power inequality for the Berezin number of an operator. Moreover, by applying some inequalities for nonnegative Hermitian forms, some vector inequalities for n-tuple operators via Berezin symbols are established.

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Acknowledgements

The authors thank to the referee for his/her very carefully reading the paper and making useful remarks and suggestions which essentially improved the presentation of the paper. The first and third authors also would like to extend his sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project no. RGP-VPP-323.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    M. Garayev & F. Bouzeffour

  2. Department of Mathematics, Suleyman Demirel University, 32260, Isparta, Turkey

    S. Saltan & B. Aktan

Authors
  1. M. Garayev
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  2. S. Saltan
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  3. F. Bouzeffour
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  4. B. Aktan
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Correspondence to S. Saltan.

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Garayev, M., Saltan, S., Bouzeffour, F. et al. Some inequalities involving Berezin symbols of operator means and related questions. RACSAM 114, 85 (2020). https://doi.org/10.1007/s13398-020-00815-5

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  • DOI: https://doi.org/10.1007/s13398-020-00815-5

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