Geodesic
A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix
Fuad Kittaneh1
1 Department of Mathematics University of Jordan Amman, Jordan
Studia Mathematica, Tome 158 (2003) no. 1, pp. 11-17

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 $$ w(A) \le \frac{1}{2} (\| A \| + \| A^2 \|^{1/2} ), $$ where $w(A)$ and $\|A\|$ are the numerical radius and the usual operator norm of $A$, respectively. An application of this inequality is given to obtain a new estimate for the numerical radius of the Frobenius companion matrix. Bounds for the zeros of polynomials are also given.
DOI : 10.4064/sm158-1-2
Keywords: shown bounded linear operator complex hilbert space frac where numerical radius usual operator norm respectively application inequality given obtain estimate numerical radius frobenius companion matrix bounds zeros polynomials given

Fuad Kittaneh 1

1 Department of Mathematics University of Jordan Amman, Jordan 
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Fuad Kittaneh. A numerical radius inequality and an estimate for the
 numerical radius of the Frobenius companion matrix. Studia Mathematica, Tome 158 (2003) no. 1, pp. 11-17. doi: 10.4064/sm158-1-2

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