Improvement of inequalities related to powers of the numerical radius

Yaser Khatib; Stanford Shateyi; Yaser Khatib; Stanford Shateyi

doi:10.3934/math.2024930

AIMS Mathematics

2024, Volume 9, Issue 7: 19089-19103. doi: 10.3934/math.2024930

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Research article

Improvement of inequalities related to powers of the numerical radius

Yaser Khatib ^{1
,
,},
Stanford Shateyi ^{2
,
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1.
Department of Mathematics, Farhangian of Bojnourd and Education (and Training) Administration of Bojnourd, Iran
2.
Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received: 09 December 2023 Revised: 29 March 2024 Accepted: 07 April 2024 Published: 07 June 2024
MSC : 47A12, 47A30, 47A63

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 $ \xi $, we provided a very good improvement for the $ \omega^r(E) $, for $ E\in \mathcal{B}(\mathcal{H}_s) $.
- positive operators,
- normalized positive linear map,
- numerical radius,
- Hilbert spaces
Citation: Yaser Khatib, Stanford Shateyi. Improvement of inequalities related to powers of the numerical radius[J]. AIMS Mathematics, 2024, 9(7): 19089-19103. doi: 10.3934/math.2024930

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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 $ \xi $, we provided a very good improvement for the $ \omega^r(E) $, for $ E\in \mathcal{B}(\mathcal{H}_s) $.

References

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