Numerical radius inequalities of operator matrices with applications

Abstract

We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space, which improve on the existing bounds. We also obtain some upper and lower bounds for the numerical radius of operator matrices and illustrate with numerical examples that these bounds are better than the existing bounds.

Refinements of A-numerical radius inequalities and their applications

“…Now, we are in a position to present our desired estimation for the bounds of the zeros of p(z). Following [6,Section 3], we list the bounds for the zeros of the polynomial p(z) to conclude that the bound obtained in Theorem 3.4 is better than the existing bounds.…”

Estimations of zeros of a polynomial using numerical radius inequalities

“…In this article, we obtain some upper bounds for the numerical radius of bounded linear operators and operator matrices. Using these bounds and the bounds obtained in [4,5,6,7,8] we obtain bounds for the radius of the disk with centre at origin that contains all the zeros of a complex monic polynomial. Also we show with numerical examples that these bounds obtained here improve on the existing bounds.…”

Annular bounds for the zeros of a polynomial from companion matrix

“…The Frobenius companion matrix plays an important link between matrix theory and the geometry of polynomials. It has been used to obtain estimations for zeros of polynomials by matrix methods, we refer to some of the recent papers [3,4,5,13] and the references therein. Also, various mathematicians have obtained annular regions containing all the zeros of a polynomial by using classical approach, we refer to [6,7,15] and references therein.…”