Improved lower bounds for numerical radius via Cartesian decomposition

Volume 33, Issue 2, pp 169--175 https://dx.doi.org/10.22436/jmcs.033.02.05

Publication Date: December 22, 2023 Submission Date: October 16, 2023 Revision Date: November 01, 2023 Accteptance Date: November 16, 2023

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Authors

F. Alrimawi - Department of Basic Sciences, Al-Ahliyya Amman University, Amman, Jordan. F. A. Abushaheen - Basic Science Department, Faculty of Arts and Educational Sciences, Middle East University, Amman, Jordan. - Applied Science Research Center, Applied Science Private University, Amman, Jordan. R. Alkhateeb - Department of Basic Sciences, Al-Ahliyya Amman University, Amman, Jordan.

Abstract

In this article, we derive various lower bounds for the numerical radius of operators that refine the well-known inequality \(w^{2}(A)\geq \frac{1}{4} \left\Vert A^{\ast }A+AA^{\ast }\right\Vert \).

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Keywords

• Numerical radius
• operator norm
• bounded linear operator

MSC

•  47A12
•  47A30
•  15A60

References

• [1] A. Abu-Omar, F. Kittaneh, A generalization of the numerical radius, Linear Algebra Appl., 569 (2019), 323–334
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] M. W. Alomari, Numerical radius inequalities for Hilbert space operators, Complex Anal. Oper. Theory, 15 (2021), 19 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] F. Alrimawi, O. Hirzallah, F. Kittaneh, Norm inequalities related to Clarkson inequalities, Electron. J. Linear Algebra, 34 (2018), 163–169
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] F. Alrimawi, O. Hirzallah, F. Kittaneh, Norm inequalities involving the weighted numerical radii of operators, Linear Algebra Appl., 657 (2023), 127–146
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] F. Alrimawi, H. Kawariq, F. A. Abushaheen, Generalized-weighted numerical radius inequalities for Schatten p-norms, Int. J. Math. Comput. Sci., 17 (2022), 1463–2022
  • View Article
  • Google Scholar
  • MATH


• [6] P. Bhunia, S. Bag, K. Paul, Bounds for zeros of a polynomial using numerical radius of Hilbert space operators, Ann. Funct. Anal., 12 (2021), 14 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] P. Bhunia, S. S. Dragomir, M. S. Moslehian, K. Paul, Lectures on numerical radius inequalities, In: Infosys Science Foundation Series in Mathematical Sciences, Springer, Cham (2022)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] P. Bhunia, S. Jana, M. S. Moslehian, K. Paul, Improved inequalities for numerical radius via Cartesian decomposition, Funct. Anal. Appl., 57 (2023), 18–28
  • View Article
  • Google Scholar
  • MATH


• [9] P. Bhunia, S. Jana, K. Paul, Refined inequalities for the numerical radius of Hilbert space operators, arXiv preprint arXiv:2106.13949, (2021), 1–12
  • View Article
  • Google Scholar


• [10] P. Bhunia, K. Paul, Some improvements of numerical radius inequalities of operators and operator matrices, Linear Multilinear Algebra, 70 (2020), 1995–2013
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] K. R. Davidson, S. C. Power, Best approximation in C-algebras, J. Reine Angew. Math., 368 (1986), 43–62
  • View Article
  • Google Scholar


• [12] K. Feki, T. Yamazaki, Joint numerical radius of spherical Aluthge transforms of tuples of Hilbert space operators, Math. Inequal. Appl., 24 (2021), 405–420
  • View Article
  • MathSciNet
  • Google Scholar


• [13] F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Math., 158 (2003), 11–17
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math., 168 (2005), 73–80
  • View Article
  • MathSciNet
  • Google Scholar


• [15] M. S. Moslehian, Q. Xu, A. Zamani, Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces, Linear Algebra Appl., 591 (2020), 299–321
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] M. E. Omidvar, H. R. Moradi, K. Shebrawi, Sharpening some classical numerical radius inequalities, Oper. Matrices, 12 (2018), 407–416
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] S. Sahoo, N. C. Rout, M. Sababheh, Some extended numerical radius inequalities, Linear Multilinear Algebra, 69 (2021), 907–920
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] M. Sattari, M. S. Moslehian, T. Yamazaki, Some generalized numerical radius inequalities for Hilbert space operators, Linear Algebra Appl., 470 (2015), 216–227
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH