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

• Autorzy: Fuad Kittaneh
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory
• 26C10: Polynomials: location of zeros
• 47A12: Numerical range, numerical radius
• 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 158
• Numer: 1
• Strony: 11-17

Daty

wydano

2003

Twórcy

autor

Fuad Kittaneh

• Department of Mathematics, University of Jordan, Amman, Jordan

Identyfikatory

DOI

10.4064/sm158-1-2