Berezin Number Inequalities via Convex Functions


Huban M. B., Başaran H., GÜRDAL M.

Filomat, vol.36, no.7, pp.2333-2344, 2022 (SCI-Expanded) 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
  • Süleyman Demirel University Affiliated: Yes

Abstract

© 2022, University of Nis. All rights reserved.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.