A novel numerical radius upper bounds for 2 × 2 operator matrices.

In this paper, we establish some numerical radius inequalities for 2 × 2 bounded linear operator defined on a complex Hilbert space. As a natural application, the existence of the all polynomial zeros is identified in a specific small disk. Moreover, we provide a refinement of an earlier numerical radius inequality due to Herzallah et al. [Numerical radius inequalities for certain 2 × 2 operator matrices. Integr Equ Oper Theory. 2011;71:129–147] and a generalization of Shebrawi's inequality [Numerical radius inequalities for certain 2 × 2 operator matrices II. Linear Algebra Appl. 2017;523:1–12]. [ABSTRACT FROM AUTHOR]