Norm and Numerical Radius Inequalities for Hilbert Space Operators

International Journal of Mathematical Modelling & Computations

مقاله 3، دوره 12، 3 (SUMMER) - شماره پیاپی 47، آذر 2022، صفحه 173-181   

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2022.1932741.1214

نویسندگان

Mohsen Erfanian Omidvar^* ؛ Mahdi Ghasvareh

Department of Mathematics, Mashhad Branch, Islamic Azad University

چکیده

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

\[\omega \left( {{B}^{*}}A \right)\le \sqrt{\frac{1}{2}{{\left\| A \right\|}^{2}}{{\left\| B \right\|}^{2}}+\frac{1}{2}\omega \left( {{\left| B \right|}^{2}}{{\left| A \right|}^{2}} \right)}\le 4\omega \left( A \right)\omega \left( B \right).\]

کلیدواژه‌ها

Bounded linear operators؛ Numerical radius؛ Operator norm؛ Inequality