A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix

Fuad Kittaneh

Studia Mathematica (2003)

  • Volume: 158, Issue: 1, page 11-17
  • ISSN: 0039-3223

Abstract

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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 | | + | | 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.

How to cite

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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 -

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