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

SALTAN S., Tapdigoglu R., Calisir I.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.52, no.5, pp.1767-1774, 2022 (SCI-Expanded) identifier 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
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

We prove new Gruss 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 ber(A(2)) <= 1/4 (ber(A(4)))+broken vertical bar broken vertical bar A(2) broken vertical bar broken vertical bar(2)Ber), where ber( center dot) and broken vertical bar broken vertical bar center dot broken vertical bar broken vertical bar Ber denote, respectively, the Berezin number and the Berezin norm of operator A.