Geodesic
Numerical radius inequalities for Hilbert space operators
Fuad Kittaneh1
1 Department of Mathematics University of Jordan Amman, Jordan
Studia Mathematica, Tome 168 (2005) no. 1, pp. 73-80

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

It is shown that if $A$ is a bounded linear operator on a complex Hilbert space, then $$ {1 \over 4}\| {A^* A + AA^* } \| \le ( {w(A )} )^2 \le {1 \over 2}\| {A^* A + AA^* }\| , $$ where $w(\cdot )$ and $\| \cdot \| $ are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities $$ {1 \over 2}\| A \| \le w( A ) \le \| A \| . $$ Numerical radius inequalities for products and commutators of operators are also obtained.
DOI : 10.4064/sm168-1-5
Keywords: shown bounded linear operator complex hilbert space * * * * where cdot cdot numerical radius usual operator norm respectively these inequalities lead considerable improvement known inequalities numerical radius inequalities products commutators operators obtained

Fuad Kittaneh 1

1 Department of Mathematics University of Jordan Amman, Jordan 
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Fuad Kittaneh. Numerical radius inequalities for Hilbert space operators. Studia Mathematica, Tome 168 (2005) no. 1, pp. 73-80. doi: 10.4064/sm168-1-5

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