Berezin Number Inequalities via Convex Functions

HUBAN M. B., Başaran H., GÜRDAL M.

Filomat, vol.36, no.7, pp.2333-2344, 2022 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2207333h
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.2333-2344
  • Keywords: Berezin number, Berezin symbol, mixed Schwarz inequality, reproducing kernel Hilbert space
  • Isparta University of Applied Sciences Affiliated: Yes

Abstract

The Berezin symbol à of an operator A on the reproducing kernel Hilbert space H (Ω) over some set Ω with the reproducing kernel kξ is defined by (Formula presented) The Berezin number of an operator A is defined by (Formula presented) We study some problems of operator theory by using this bounded function Ã, including treatments of inner product inequalities via convex functions for the Berezin numbers of some operators. We also establish some inequalities involving of the Berezin inequalities.