Optimizing Numerical Radius Inequalities via Decomposition Techniques and Parameterized Aluthge Transforms

  • Jamal Oudetallah Department of Mathematics, University of Petra, Amman 11196, Jordan
  • Mutaz Shatnawi Department of Mathematics, Irbid National University, Irbid 21110, Jordan
  • Ala Amourah Faculty of Education and Arts, Sohar University, Sohar 3111, Oman
  • Abdullah Alsoboh Department of Basic and Applied Sciences, College of Applied and Health Sciences, A’Sharqiyah University, Post Box No. 42, Post Code No. 400, Ibra, Sultanate of Oman
  • Iqbal M. Batiha Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE
  • Tala Sasa Applied Science Research Center, Applied Science Private University, Amman, Jordan
DOI: https://doi.org/10.19139/soic-2310-5070-2645
Keywords: Numerical radius, Aluthge transform, Spectral radius, Matrix analysis, Hilbert space operators, Operator norm, Hyponormal operators, Quasi-normal operators

Abstract

This manuscript presents substantial refinements to several classical inequalities connecting the numerical radius w(V), spectral radius ρ(V), and operator norm ∥V∥ for bounded linear operators acting on Hilbert spaces. Building upon inequalities established by Kittaneh 1 and the framework introduced by Yamazaki 3 , we develop enhanced bounds through parameterized Aluthge transforms and contemporary decomposition methods. Our key contributions encompass: (1) refined numerical radius bounds that strengthen Kittaneh’s inequality through quantifiable correction terms, (2) parameterized spectral radius inequalities for operator sums and products that significantly improve existing results, and (3) precision-enhanced bounds for commutators and anti-commutators. We provide comprehensive proofs establishing the superiority of our bounds across diverse operator classes. These refinements yield important theoretical implications in operator theory and matrix analysis, offering substantially tighter estimations of operator spread than previously attainable results.
Published
2025-07-07
How to Cite
Oudetallah, J., Shatnawi, M., Amourah, A., Alsoboh, A., Iqbal M. Batiha, & Sasa, T. (2025). Optimizing Numerical Radius Inequalities via Decomposition Techniques and Parameterized Aluthge Transforms. Statistics, Optimization & Information Computing, 14(3), 1326-1336. https://doi.org/10.19139/soic-2310-5070-2645
Issue
Vol 14 No 3 (2025)
Section
Research Articles
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