ABSTRACT

In this paper, we establish some numerical radius inequalities for $2\times 2$ 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 $2\times 2$ operator matrices. Integr Equ Oper Theory. 2011;71:129–147] and a generalization of Shebrawi's inequality [Numerical radius inequalities for certain $2\times 2$ operator matrices II. Linear Algebra Appl. 2017;523:1–12].

摘要

在本文中，我们建立了一些数值半径不等式$2\times 2$定义在复希尔伯特空间上的有界线性算子。作为一个自然的应用，所有多项式零的存在都在一个特定的小磁盘中被识别出来。此外，由于 Herzallah 等人，我们提供了对早期数值半径不等式的改进。[某些数值半径不等式$2\times 2$算子矩阵。Integr Equ Oper 理论。2011;71:129–147] 和 Shebrawi 不等式的概括 [Numerical radius inequalities for certain$2\times 2$算子矩阵 II。线性代数应用程序。2017;523:1-12]。