Volume 26 , Issue 2 , PP: 279-291, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
M. Abu Saleem 1 , Khalid Shebrawi 2 * , Tasnim Alkharabsheh 3
Doi: https://doi.org/10.54216/IJNS.260221
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 .
Numerical radius , Spectral norm , Hilbert Schmidt norm , Hermitian operator , Positive operator , Inequality
[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.
