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It is shown that if A is a bounded linear operator on a complex Hilbert space, then
,
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.
Fuad Kittaneh. "A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix." Studia Mathematica 158.1 (2003): 11-17. <http://eudml.org/doc/285150>.
@article{FuadKittaneh2003, abstract = {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.}, author = {Fuad Kittaneh}, journal = {Studia Mathematica}, keywords = {numerical radius; operator norm; positive operator; Frobenius companion matrix; bounds for the zeros of polynomials}, language = {eng}, number = {1}, pages = {11-17}, title = {A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix}, url = {http://eudml.org/doc/285150}, volume = {158}, year = {2003}, }
TY - JOUR AU - Fuad Kittaneh TI - A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix JO - Studia Mathematica PY - 2003 VL - 158 IS - 1 SP - 11 EP - 17 AB - 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. LA - eng KW - numerical radius; operator norm; positive operator; Frobenius companion matrix; bounds for the zeros of polynomials UR - http://eudml.org/doc/285150 ER -