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

  • Nəşrin Növü: Article / Article
  • Cild: 52 Say: 5
  • Nəşr tarixi: 2022
  • Doi nömrəsi: 10.1216/rmj.2022.52.1767
  • jurnalın adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Səhifə sayı: pp.1767-1774
  • Adres: Yox

Qısa məlumat

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.