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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 26Issue 2PP: 279-291 • 2025

On the generalized numerical radii of operators

M. Abu Saleem 1* ,
Khalid Shebrawi 1 ,
Tasnim Alkharabsheh 1
1Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan
* Corresponding Author.
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© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: January 07, 2025 Revised: February 09, 2025 Accepted: March 13, 2025

Abstract

It is shown that if A, B,X, and Y are operators acting on a finite dimensional Hilbert space, then. ωu (AXB∗ ± BYA∗) ≤ 2 ∥A∥ ∥B∥ ωu ([0 X, Y 0]) where ωu (T ), ∥T ∥, are, respectively, the U-numerical radius, the spectral norm, of an operator T .

Keywords

Numerical radius Spectral norm Hilbert Schmidt norm Hermitian operator Positive operator Inequality

References

[1] A. Aldalabih, F. Kittaneh, Hilbert-Schmidt numerical radius inequalities for operator matrices, Linear Algebra Appl. 581 (2019) 72-84.

[2] S. Jana, P. Bhunia, and K. Paul, ”Euclidean operator radius and numerical radius inequalities,” arXiv preprint arXiv:2308.09252, (2023)

[3] K. Feki, ”Some athbbA-numerical radius inequalities for d¨imesd operator matrices,” arXiv preprint arXiv:2003.14378, (2020)

[4] N. C. Rout, S. Sahoo, and D. Mishra, ”On A-numerical radius inequalities for 2¨imes2 operator matrices,” arXiv preprint arXiv:2004.07494(2020)

[5] R. Bhatia, Matrix Analysis, Springer-Verlag, New York, (1997).

[6] C. K. Fong and J. A. R. Holbrook, Unitarily invariant operator norms, Canad. J. Math. 35 (1983) 274– 299.

[7] O. Hirzallah and F. Kittaneh, Numerical radius inequalities for several operators, Math. Scand. 114 (2014) 110–119.

[8] M. Ito, H. Nakazato, K. Okubo and T. Yamazaki, On generalized numerical range of the Aluthge transformation, Linear Algebra Appl. 370 (2003) 147–161.

[9] T. Yamazaki, On upper and lower bounds of the numerical radius and an equality condition, Studia Math. 178 (2007) 83-89.

[10] A. Zamani, A-numerical radius inequalities for semi-Hilbertian space operators, Linear Algebra Appl. 578 (2019) 159–183.

 

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Saleem, M. Abu, Shebrawi, Khalid, Alkharabsheh, Tasnim. "On the generalized numerical radii of operators." International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 2, 2025, pp. 279-291. DOI: https://doi.org/10.54216/IJNS.260221
Saleem, M., Shebrawi, K., Alkharabsheh, T. (2025). On the generalized numerical radii of operators. International Journal of Neutrosophic Science, Volume 26(Issue 2), 279-291. DOI: https://doi.org/10.54216/IJNS.260221
Saleem, M. Abu, Shebrawi, Khalid, Alkharabsheh, Tasnim. "On the generalized numerical radii of operators." International Journal of Neutrosophic Science Volume 26, no. Issue 2 (2025): 279-291. DOI: https://doi.org/10.54216/IJNS.260221
Saleem, M., Shebrawi, K., Alkharabsheh, T. (2025) 'On the generalized numerical radii of operators', International Journal of Neutrosophic Science, Volume 26(Issue 2), pp. 279-291. DOI: https://doi.org/10.54216/IJNS.260221
Saleem M, Shebrawi K, Alkharabsheh T. On the generalized numerical radii of operators. International Journal of Neutrosophic Science. 2025;Volume 26(Issue 2):279-291. DOI: https://doi.org/10.54216/IJNS.260221
M. Saleem, K. Shebrawi, T. Alkharabsheh, "On the generalized numerical radii of operators," International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 2, pp. 279-291, 2025. DOI: https://doi.org/10.54216/IJNS.260221
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