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

• Published in: Numerical functional analysis and optimization Vol. 44; no. 9; pp. 970 - 986
• Main Authors: Bhunia, P., Gürdal, M., Paul, K., Sen, A., Tapdigoglu, R.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.07.2023; Taylor & Francis Ltd
• Subjects: Berezin norm; Berezin radius; bounded linear operator; Hilbert space; Inequalities; Kernels; Linear operators; Primary: 47A30, 47A12; reproducing kernel Hilbert space; Secondary: 47A63, 15A60
• ISSN: 0163-0563; 1532-2467
• DOI: 10.1080/01630563.2023.2221857

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.