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

SALTAN S., Tapdigoglu R., Çalisir I.

Rocky Mountain Journal of Mathematics, cilt.52, sa.5, ss.1767-1774, 2022 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 52 Sayı: 5
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1216/rmj.2022.52.1767
  • Dergi Adı: Rocky Mountain Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.1767-1774
  • Anahtar Kelimeler: Berezin symbol, reproducing kernel Hilbert space, Berezin number, Berezin norm, positive operator, Cebycev functional, self-adjoint operator, CEBYSEVS TYPE INEQUALITIES, HILBERT-SPACE, REPRODUCING KERNELS, SYMBOL, QUESTIONS
  • Süleyman Demirel Üniversitesi Adresli: Evet

Özet

© 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.