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

Bhunia, P and Gürdal, M and Paul, K and Sen, A and Tapdigoglu, R (2023) On a New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Radius Inequalities. In: Numerical Functional Analysis and Optimization .

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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.

Item Type:	Journal Article
Publication:	Numerical Functional Analysis and Optimization
Publisher:	Taylor and Francis Ltd.
Additional Information:	The copyright for this article belongs to the Taylor and Francis Ltd.
Keywords:	Berezin norm; Berezin radius; bounded linear operator; reproducing kernel Hilbert space
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	14 Jul 2023 06:15
Last Modified:	08 Aug 2023 10:40
URI:	https://eprints.iisc.ac.in/id/eprint/82477

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