A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix
Volume 158 / 2003
Studia Mathematica 158 (2003), 11-17
MSC: 15A60, 26C10, 30C15, 47A12, 47A30.
DOI: 10.4064/sm158-1-2
Abstract
It is shown that if $A$ is a bounded linear operator on a complex Hilbert space, then $$ w(A) \le \frac{1}{2} (\| A \| + \| A^2 \|^{1/2} ), $$ 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.
