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

摘要

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 applicati