Open Access

# On some numerical radius inequalities for Hilbert space operators

### Abstract

This article is devoted to studying some new numerical radius inequalities for Hilbert space operators. Our analysis enables us to improve an earlier bound for numerical radius due to Kittaneh. It is shown, among other, that if $A\in \mathcal{B}(\mathcal{H})$, then $\frac{1}{8}\left( {{\left\| A+{{A}^{*}} \right\|}^{2}}+{{\left\| A-{{A}^{*}} \right\|}^{2}} \right)\le \omega ^{2}\left( A \right) \le \left\| \frac{{{\left| A \right|}^{2}}+{{\left| {{A}^{*}} \right|}^{2}}}{2} \right\|-m\left( {{\left( \frac{\left| A \right|-\left| {{A}^{*}} \right|}{2} \right)}^{2}} \right ).$

Отримані нові нерівності для числового радіуса операторів у гільбертовім просторі. Зокрема, покращено попередній результат Кіттане. Показано, що для $A\in B(H)$, $\frac{1}{8}\left( {{\left\| A+{{A}^{*}} \right\|}^{2}}+{{\left\| A-{{A}^{*}} \right\|}^{2}} \right)\le \omega ^{2}\left( A \right) \le \left\| \frac{{{\left| A \right|}^{2}}+{{\left| {{A}^{*}} \right|}^{2}}}{2} \right\|-m\left( {{\left( \frac{\left| A \right|-\left| {{A}^{*}} \right|}{2} \right)}^{2}} \right ).$

Key words: Numerical radius, norm inequality, convex function.

### Article Information

 Title On some numerical radius inequalities for Hilbert space operators Source Methods Funct. Anal. Topology, Vol. 27 (2021), no. 2, 192-197 DOI 10.31392/MFAT-npu26_2.2021.07 MathSciNet MR4296407 Milestones Received 21/09/2020; Revised 15/03/2021 Copyright The Author(s) 2021 (CC BY-SA)

### Authors Information

Mahdi Ghasvareh
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Mohsen Erfanian Omidvar
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

### Citation Example

Mahdi Ghasvareh and Mohsen Erfanian Omidvar, On some numerical radius inequalities for Hilbert space operators, Methods Funct. Anal. Topology 27 (2021), no. 2, 192-197.

### BibTex

@article {MFAT1564,
AUTHOR = {Mahdi Ghasvareh and Mohsen Erfanian Omidvar},
TITLE = {On some numerical radius inequalities for Hilbert space operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {27},
YEAR = {2021},
NUMBER = {2},
PAGES = {192-197},
ISSN = {1029-3531},
MRNUMBER = {MR4296407},
DOI = {10.31392/MFAT-npu26_2.2021.07},
URL = {http://mfat.imath.kiev.ua/article/?id=1564},
}

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