Improved upper bounds for the Berezin numbers of operators on reproducing kernel Hilbert spaces

Riddhick Birbonshi; Sumon Ghosh; Fuad Kittaneh; Saikat Mahapatra; Sarita Ojha

Improved upper bounds for the Berezin numbers of operators on reproducing kernel Hilbert spaces

Functional Analysis 2026-07-14 v1

Authors: Riddhick Birbonshi , Sumon Ghosh , Fuad Kittaneh , Saikat Mahapatra , Sarita Ojha

Abstract

In this article, several upper bounds for the Berezin numbers of bounded linear operators on reproducing kernel Hilbert spaces are obtained through the use of interpolation paths of symmetric means and Orlicz functions. With suitable selections of these paths and functions, we show that the results presented here refine and generalize several earlier known findings. Furthermore, we derive some Berezin number inequalities for such operators using refined Young's inequalities.

Keywords

Berezin number reproducing kernel Hilbert space interpolation path Orlicz function Young inequality upper bound

Cite

@article{arxiv.2607.12537,
  title  = {Improved upper bounds for the Berezin numbers of operators on reproducing kernel Hilbert spaces},
  author = {Riddhick Birbonshi and Sumon Ghosh and Fuad Kittaneh and Saikat Mahapatra and Sarita Ojha},
  journal= {arXiv preprint arXiv:2607.12537},
  year   = {2026}
}