SOME NEW RELATIONS BETWEEN THE BEREZIN NUMBER AND THE BEREZIN NORM OF OPERATORS

SALTAN S., Tapdigoglu R., Çalisir I.

Rocky Mountain Journal of Mathematics, vol.52, no.5, pp.1767-1774, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1216/rmj.2022.52.1767
  • Journal Name: Rocky Mountain Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1767-1774
  • Keywords: Berezin norm, Berezin number, Berezin symbol, positive operator, reproducing kernel Hilbert space, self-adjoint operator, Čebyčev functional
  • Süleyman Demirel University Affiliated: Yes

Abstract

© Rocky Mountain Mathematics Consortium.We prove new Grüss type inequalities for the Berezin symbol of some operator products. As biproducts, we find new relations between the Berezin number, the Berezin norm and some new quantities for operators acting on the reproducing kernel Hilbert space. In particular, we prove for arbitrary bounded linear operator A that (Equation presented), where ber(· ) and ∥ · ∥Ber denote, respectively, the Berezin number and the Berezin norm of operator A.