Numerical radius inequalities and its applications in estimation of zeros of polynomials

TL;DR

This paper develops improved bounds for the numerical radius of operators and applies these results to more accurately estimate the zeros of polynomials, enhancing existing methods.

Contribution

It introduces new upper and lower bounds for the numerical radius and applies these bounds to improve polynomial zero estimations.

Findings

Enhanced bounds for the numerical radius of operators

A new upper bound for the spectral radius of operator sums

More accurate estimation of polynomial zeros

Abstract

We present some upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improves on the existing upper and lower bounds. We also present an upper bound for the spectral radius of sum of product of $n$ pairs of operators. As an application of the results obtained, we provide a better estimation for the zeros of a given polynomial.