Abstract

We introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the AA-numerical radius and AA-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 AA-numerical radius of semi-Hilbertian space operators, which are sharper than the earlier ones.

Author information

Contact details are reproduced from the original publication and may be historical.

Kallol Paul

Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India

kalloldada@gmail.com

Keywords

  • A-numerical radius
  • A-operator semi-norm
  • semi-Hilbertian space
  • inequality

Mathematics Subject Classification

47A12; 47A30, 47A63

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Suggested citation

P. Bhunia, A. Sen, K. Paul. “New Semi-Norm of Semi-Hilbertian Space Operators and its Application.” Journal of Convex Analysis 29 (2022), No. 4, 1149–1160. https://doi.org/10.68381/jca29063

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press.