LAUSR

In this paper, we implement the improvement of numerical radius inequalities that were produced by Alomari MW. [Refinements of some numerical radius inequalities for Hilbert space operators. Linear and Multilinear Algebra. 2019 Jun 4:1-6] and devise a new upper bound for 2× 2 operator matrices on complex Hilbert space with many examples which show that our bound is sharper than the existing bounds proved by Bani-Domi W, Kittaneh F. [Norm and numerical radius inequalities for Hilbert space operators. Linear and Multilinear Algebra. 2020 Jul 28:1-2], Al-Dolat M, Jaradat I, Al-Husban B. A novel numerical radius upper bounds for 2× 2 operator matrices. Linear and Multilinear Algebra. 2020 Apr 23:1-2], Shebrawi K. [Numerical radius inequalities for certain 2× 2 operator matrices II. Linear Algebra and its Applications. 2017 Jun 15; 523:1-2] and Hirzallah O, Kittaneh F, Shebrawi K. [Numerical radius inequalities for 2×2 operator matrices. Studia Mathematica. 2012; 210:99-115]. Mathematics subject classification (2020): 47A12, 47A30, 47A63, 47B33.