A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix
Fuad Kittaneh
Studia Mathematica, Tome 157 (2003), p. 11-17 / Harvested from The Polish Digital Mathematics Library
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It is shown that if A is a bounded linear operator on a complex Hilbert space, then w(A)≤1/2(||A||+||A²||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.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:285150 
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     year = {2003},
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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 157 (2003) pp. 11-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm158-1-2/