On a New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Radius Inequalities

Bhunia P., GÜRDAL M., Paul K., Sen A., Tapdigoglu R.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.44, no.9, pp.970-986, 2023 (SCI-Expanded) identifier identifier

  • 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
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

In this paper, we provide a new norm(a-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 a-Berezin norm and develop various inequalities involving the a-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.