On a New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Radius Inequalities
Pintu Bhunia, Mehmet Gürdal, Kallol Paul, Arzu Şen, Ramiz Tapdıgoglu
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.
Topics & Concepts
MathematicsHilbert spaceNorm (philosophy)Operator normBounded functionReproducing kernel Hilbert spacePure mathematicsLinear operatorsMathematical analysisDual normBounded operatorBanach spaceLawPolitical scienceMathematical Inequalities and ApplicationsMatrix Theory and AlgorithmsHolomorphic and Operator Theory