Some New Inequalities via Berezin Numbers

HUBAN M. B., Başaran H., GÜRDAL M.

Turkish Journal of Mathematics and Computer Science, vol.14, no.1, pp.129-137, 2022 (Scopus, TRDizin) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.47000/tjmcs.1014841
  • Journal Name: Turkish Journal of Mathematics and Computer Science
  • Journal Indexes: Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.129-137
  • Keywords: Berezin radius, Berezin transform, Jensen’s inequality, mixed Schwarz inequality, Reproducing kernel Hilbert space
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

The Berezin transform T and the Berezin radius of an operator T on the reproducing kernel Hilbert space H (Q) over some set Q with the reproducing kernel Kη are defined, respectively, by (Formula Presented) We study several sharp inequalities by using this bounded function ˜T, involving powers of the Berezin radius and the Berezin norms of reproducing kernel Hilbert space operators. We also give some inequalities regarding the Berezin transforms of sum of two operators.