INEQUALITIES RELATED TO BEREZIN NORM AND BEREZIN NUMBER OF OPERATORS

Başaran H., HUBAN M. B., GÜRDAL M.

Bulletin of Mathematical Analysis and Applications, vol.14, no.2, pp.1-11, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.54671/bmaa-2022-2-1
  • Journal Name: Bulletin of Mathematical Analysis and Applications
  • Journal Indexes: Scopus
  • Page Numbers: pp.1-11
  • Keywords: Berezin norm, Berezin number, Hermite-Hardamard inequality, numerical radius, operator convex function, reproducing kernel Hilbert space
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

The Berezin symbol A of an operator A on the reproducing kernel Hilbert space H (Ω) over some set Ω with the reproducing kernel kλ is defined By (Formula Presented) In this paper, we obtain some new inequalities for Berezin symbols of operators on reproducing kernel Hilbert spaces by using classical Hermite-Hadamard inequality and convex functions. Some other related questions are also discussed.