Some New Inequalities via Berezin Numbers
Turkish Journal of Mathematics and Computer Science, vol.14, no.1, pp.129-137, 2022 (Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 14 Issue: 1
- Publication Date: 2022
- Doi Number: 10.47000/tjmcs.1014841
- Journal Name: Turkish Journal of Mathematics and Computer Science
- Journal Indexes: Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.129-137
- Keywords: Berezin radius, Berezin transform, Jensen’s inequality, mixed Schwarz inequality, Reproducing kernel Hilbert space
- Isparta University of Applied Sciences Affiliated: Yes
Abstract
The Berezin transform T and the Berezin radius of an operator T on the reproducing kernel Hilbert space H (Q) over some set Q with the reproducing kernel Kη are defined, respectively, by (Formula Presented) We study several sharp inequalities by using this bounded function ˜T, involving powers of the Berezin radius and the Berezin norms of reproducing kernel Hilbert space operators. We also give some inequalities regarding the Berezin transforms of sum of two operators.