10.30495/ijm2c.2022.1932741.1214

Norm and Numerical Radius Inequalities for Hilbert Space Operators

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  • Mohsen Omidvar*1,
  • Mahdi Ghasvareh1,
  1. Department of Mathematics, Mashhad Branch, Islamic Azad University

Received: 08-06-2021

Accepted: 31-01-2022

Published in Issue 01-09-2022

Copyright (c) 2024 International Journal of Mathematical Modeling & Computations

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Omidvar, M., & Ghasvareh, M. (2022). Norm and Numerical Radius Inequalities for Hilbert Space Operators. International Journal of Mathematical Modelling & Computations, 12(3), 173-181. https://doi.org/10.30495/ijm2c.2022.1932741.1214
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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\[\omega \left( {{B}^{*}}A \right)\le \sqrt{\frac{1}{2}{{\left\| A \right\|}^{2}}{{\left\| B \right\|}^{2}}+\frac{1}{2}\omega \left( {{\left| B \right|}^{2}}{{\left| A \right|}^{2}} \right)}\le 4\omega \left( A \right)\omega \left( B \right).\]
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