On a New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Radius Inequalities
Numerical Functional Analysis and Optimization, vol.44, no.9, pp.970-986, 2023 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 44 Issue: 9
- Publication Date: 2023
- Doi Number: 10.1080/01630563.2023.2221857
- Journal Name: Numerical Functional Analysis and Optimization
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
- Page Numbers: pp.970-986
- Keywords: Berezin norm, Berezin radius, bounded linear operator, reproducing kernel Hilbert space
- Süleyman Demirel University Affiliated: Yes
Abstract
In this paper, we provide a new norm(α-Berezin norm) on the space of all bounded linear operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin radius and the Berezin norm. We study the basic properties of the α-Berezin norm and develop various inequalities involving the α-Berezin norm. By using the inequalities we obtain various bounds for the Berezin radius of bounded linear operators, which improve on the earlier bounds. Further, we obtain a Berezin radius inequality for the sum of the product of operators, from which we derive new Berezin radius bounds.