On Further Accurate Estimates for the Numerical Radii of Operators

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Fadi Alrimawi, Ahmad Al-Natoor

Abstract

In this paper, we obtain some upper bounds for numerical radius of operators which generalize some well-known inequalities for classical numerical radius and refine some recent inequalities concerning the numerical radius inequalities of Hilbert space operators.

Article Details

References

  1. M.W. Alomari, On Cauchy-Schwarz Type Inequalities and Applications to Numerical Radius Inequalities, arXiv:2009.01839, 2020. https://doi.org/10.48550/arXiv.2009.01839.
  2. M.W. Alomari, Numerical Radius Inequalities for Hilbert Space Operators, Complex Anal. Oper. Theory 15 (2021), 111. https://doi.org/10.1007/s11785-021-01161-z.
  3. F. Alrimawi, Some Singular Value Inequalities for Convex Functions of Matrices, Int. J. Anal. Appl. 24 (2026), 55. https://doi.org/10.28924/2291-8639-24-2026-55.
  4. F. Alrimawi, H. Kawariq, On Some Generalized Numerical Radius Inequalities for Hilbert Space Operators, J. Math. Comput. Sci. 32 (2023), 257–262. https://doi.org/10.22436/jmcs.032.03.06.
  5. F. Alrimawi, F.A. Abushaheen, R. Alkhateeb, Improved Lower Bounds for Numerical Radius via Cartesian Decomposition, J. Math. Comput. Sci. 33 (2023), 169–175. https://doi.org/10.22436/jmcs.033.02.05.
  6. F. Alrimawi, H. Kawariq, F.A. Abushaheen, Generalized-Weighted Numerical Radius Inequalities for Schatten $p$-Norms, Int. J. Math. Comput. Sci. 17 (2022), 1463–1473.
  7. F. Alrimawi, O. Hirzallah, F. Kittaneh, Norm Inequalities Involving the Weighted Numerical Radii of Operators, Linear Algebr. Appl. 657 (2023), 127–146. https://doi.org/10.1016/j.laa.2022.10.018.
  8. P. Bhunia, K. Paul, Some Improvements of Numerical Radius Inequalities of Operators and Operator Matrices, Linear Multilinear Algebr. 70 (2020), 1995–2013. https://doi.org/10.1080/03081087.2020.1781037.
  9. Y. Chen, Y. Wei, Numerical Radius for the Asymptotic Stability of Delay Differential Equations, Linear Multilinear Algebr. 65 (2016), 2306–2315. https://doi.org/10.1080/03081087.2016.1273313.
  10. M.T. Chien, H. Nakazato, Perturbation of the Q-Numerical Radius of a Weighted Shift Operator, J. Math. Anal. Appl. 345 (2008), 954–963. https://doi.org/10.1016/j.jmaa.2008.05.015.
  11. S.S. Dragomir, Power Inequalities for the Numerical Radius of a Product of Two Operators in Hilbert Spaces, Sarajev. J. Math. 5 (2024), 269–278. https://doi.org/10.5644/sjm.05.2.10.
  12. T. Furuta, A Simplified Proof of Heinz Inequality and Scrutiny of Its Equality, Proc. Am. Math. Soc. 97 (1986), 751–753. https://doi.org/10.1090/s0002-9939-1986-0846001-3.
  13. J. Pecaric, T. Furuta, J.M. Hot, Y. Seo, Mond-Pecaric Method in Operator Inequalitie, Element Publishing House, Zagreb, Croatia, 2005.
  14. K. He, J.C. Hou, Applying the Theory of Numerical Radius of Operators to Obtain Multi-Observable Quantum Uncertainty Relations, Acta Math. Sin. Engl. Ser. 38 (2022), 1241–1254. https://doi.org/10.1007/s10114-022-1474-y.
  15. F. Kittaneh, A Numerical Radius Inequality and an Estimate for the Numerical Radius of the Frobenius Companion Matrix, Stud. Math. 158 (2003), 11–17. https://doi.org/10.4064/sm158-1-2.
  16. F. Kittaneh, Numerical Radius Inequalities for Hilbert Space Operators, Studia Math. 168 (2005), 73–80.
  17. H.R. Moradi, M. Sababheh, More Accurate Numerical Radius Inequalities (II), Linear Multilinear Algebr. 69 (2019), 921–933. https://doi.org/10.1080/03081087.2019.1703886.
  18. H.R. Moradi, F. Alrimawi, M. Sababheh, New Norm and Numerical Radius Bounds via Advanced Cauchy-Schwarz Inequalities, Ann. Univ. Ferrara 72 (2026), 20. https://doi.org/10.1007/s11565-026-00644-1.
  19. T. Qawasmeh, A. Qazza, R. Hatamleh, M.W. Alomari, R. Saadeh, Further Accurate Numerical Radius Inequalities, Preprint, (2023). https://doi.org/10.20944/preprints202304.1255.v1.
  20. M. Sababheh, H.R. Moradi, More Accurate Numerical Radius Inequalities (I), Linear Multilinear Algebr. 69 (2019), 1964–1973. https://doi.org/10.1080/03081087.2019.1651815.
  21. M. Sattari, M.S. Moslehian, T. Yamazaki, Some Generalized Numerical Radius Inequalities for Hilbert Space Operators, Linear Algebr. Appl. 470 (2015), 216–227. https://doi.org/10.1016/j.laa.2014.08.003.
  22. G. Vinti, L. Zampogni, Approximation by Means of Nonlinear Kantorovich Sampling Type Operators in Orlicz Spaces, J. Approx. Theory 161 (2009), 511–528. https://doi.org/10.1016/j.jat.2008.11.011.
  23. M.S. Yaseen, F. Alrimawi, H. Ibrahim, Modeling Sentence Meaning Using Linear Operators in a Vector Space Semantics Framework: An Interdisciplinary Approach, Forum Linguist. Stud. 7 (2025), 891–898. https://doi.org/10.30564/fls.v7i5.9553.