SOME NEW RELATIONS BETWEEN THE BEREZIN NUMBER AND THE BEREZIN NORM OF OPERATORS
Rocky Mountain Journal of Mathematics, vol.52, no.5, pp.1767-1774, 2022 (SCI-Expanded, Scopus)
- 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 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 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.