Journal of Convex Analysis 29 (2022), No. 4, 1149--1160
Copyright Heldermann Verlag 2022
New Semi-Norm of Semi-Hilbertian Space Operators and its Application
Pintu Bhunia
Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India
pintubhunia5206@gmail.com
Anirban Sen
Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India
anirbansenfulia@gmail.com
Kallol Paul
Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India
kalloldada@gmail.com
We introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the A-numerical radius and A-operator semi-norm. We study the basic properties of this semi-norm, including upper and lower bounds for it. As an application of this new semi-norm, we obtain upper bounds for the A-numerical radius of semi-Hilbertian space operators, which are sharper than the earlier ones.
Keywords: A-numerical radius, A-operator semi-norm, semi-Hilbertian space, inequality.
MSC: 47A12; 47A30, 47A63.
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