Berezin number inequalities in terms of Specht’s ratio Specht Oranına Göre Berezin Sayı Eşitsizlikleri

GÜRDAL M., Başaran H.

El-Cezeri Journal of Science and Engineering, vol.9, no.4, pp.1201-1214, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.31202/ecjse.1131830
  • Journal Name: El-Cezeri Journal of Science and Engineering
  • Journal Indexes: Scopus
  • Page Numbers: pp.1201-1214
  • Keywords: Berezin number, Hilbert functional space, positive operator, Specht’s ratio
  • Süleyman Demirel University Affiliated: Yes

Abstract

Smooth functions are associated with operators on Hilbert spaces of analytic functions through the Berezin transform. The Berezin symbol and the Berezin number of an operator A on the Hilbert functional space ℋ(Ω) over some set Ω with the reproducing kernel are defined, respectively, by (Formula presented) By using this bounded function Ã, we present some new Berezin number inequalities of Hilbert functional space operators. Some inequalities with respect to Specht’s ratio are improved and generalized. Using these modifications, we also establish various new inequalities for the Berezin radius and Berezin norm of operators.