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2021 New Estimates on Numerical Radius and Operator Norm of Hilbert Space Operators
Mahmoud HASSANI, Mohsen Erfanian OMIDVAR, Hamid Reza MORADI
Tokyo J. Math. Advance Publication 1-11 (2021). DOI: 10.3836/tjm/1502179337

Abstract

The main goal of this article is to present a new approach, made up of integrals, to refine some numerical radius inequalities. Let $A$ be a bounded linear operator on a complex Hilbert space. If $1\le r\le 2$, it is shown that \[{{\omega }^{2r}}\left( A \right)\le \left\| \int_{0}^{1}{{{\left( \left( 1-t \right)\left( \frac{{{\left| A \right|}^{2}}+{{\left| {{A}^{*}} \right|}^{2}}}{2} \right)+t\omega \left( {{A}^{2}} \right)I \right)}^{r}}dt} \right\|\,.\] Here $\omega \left( \cdot \right)$, $\left\| \cdot \right\|$ are the numerical radius and the usual operator norm, $\left| A \right|={{\left( {{A}^{*}}A \right)}^{{1}/{2}\;}}$, and $I$ is the identity operator.

Citation

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Mahmoud HASSANI. Mohsen Erfanian OMIDVAR. Hamid Reza MORADI. "New Estimates on Numerical Radius and Operator Norm of Hilbert Space Operators." Tokyo J. Math. Advance Publication 1 - 11, 2021. https://doi.org/10.3836/tjm/1502179337

Information

Published: 2021
First available in Project Euclid: 11 December 2020

Digital Object Identifier: 10.3836/tjm/1502179337

Subjects:
Primary: 47A12
Secondary: 15A60, 47A30

Rights: Copyright © 2021 Publication Committee for the Tokyo Journal of Mathematics

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