Norm and Numerical Radius Inequalities for Hilbert Space Operators

Subject Areas : International Journal of Mathematical Modelling & Computations

Mohsen Omidvar ¹ , Mahdi Ghasvareh ²

1 - Department of Mathematics, Mashhad Branch, Islamic Azad University
2 - Department of Mathematics, Mashhad Branch, Islamic Azad University

Received: 2021-06-08 Accepted : 2022-01-31 Published : 2022-09-01

Keywords: Inequality, numerical radius, operator norm, Bounded linear operators,

Abstract :

In this paper, we present several numerical radius and norm inequalities for sum of Hilbert space operators. These inequalities improve some earlier related inequalities. For $A,B\in B\left( H \right)$, we prove that\[\omega \left( {{B}^{*}}A \right)\le \sqrt{\frac{1}{2}{{\left\| A \right\|}^{2}}{{\left\| B \right\|}^{2}}+\frac{1}{2}\omega \left( {{\left| B \right|}^{2}}{{\left| A \right|}^{2}} \right)}\le 4\omega \left( A \right)\omega \left( B \right).\]