MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
REFINING NUMERICAL RADIUS INEQUALITIES OF HILBERT SPACE OPERATORS
M. A. S. Khorasani, Z. Heydarbeygi

Abstract

Several upper estimates for the numerical radius of Hilbert space operators are given. Among many other inequalities, it is shown that \begin{align*}{{\omega }^{2}}\left( A \right)\le \frac{1}{4}\left\| {{\left| A \right|}^{2}}+{{\left| {{A}^{*}} \right|}^{2}} \right\| +\frac{1}{2}\omega \left( {{A}^{2}} \right)-\frac{1}{2}\underset{\left\| x \right\|=1} {\mathop{\underset{x\in \mathscr H}{\mathop{\inf }}\,}}\,{{\left( \sqrt{\left\langle {{\left| A \right|}^{2}}x,x \right\rangle } -\sqrt{\left\langle {{\left| {{A}^{*}} \right|}^{2}}x,x \right\rangle } \right)}^{2}}.\end{align*}

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Keywords: Numerical radius; operator norm; inequality.

MSC: 47A12, 47A30

DOI: 10.57016/MV-mrhd2011

Pages:  50--57     

Volume  75 ,  Issue  1 ,  2023