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Research Article | Open Access

Improvement of inequalities related to powers of the numerical radius

Department of Mathematics, Farhangian of Bojnourd and Education (and Training) Administration of Bojnourd, Iran
Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa
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Abstract

We presented some improvements of the inequalities involving the numerical radius powers for products and sums of the operators investigated in the Hilbert space. We generalized and improved numerical radius inequalities with a generalization of the mixed Schwarz inequality. Among other things, with the help of a fraction and its power, as well as the introduction of ξ, we provided a very good improvement for the ω r ( E ), for E ∈ B ( H s ).

Keywords

positive operatorsnormalized positive linear mapnumerical radiusHilbert spaces
CLC number: 47A12, 47A30, 47A63

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 19089-19103
DOI: 10.3934/math.2024930

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Khatib Y, Shateyi S. Improvement of inequalities related to powers of the numerical radius. AIMS Mathematics, 2024, 9(7): 19089-19103. https://doi.org/10.3934/math.2024930

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Received: 09 December 2023
Revised: 29 March 2024
Accepted: 07 April 2024
Published: 15 July 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)