论文标题
适当改善众所周知的数值半径不平等及其应用
Proper improvement of well-known numerical radius inequalities and their applications
论文作者
论文摘要
给出了在复杂的Hilbert Space $ \ Mathcal {H} $上定义的有限线性运算符的数值半径的新不等式。特别是，确定如果$ t $是希尔伯特太空上的有限线性运算符$ \ mathcal {h} $，则\ [w^2（t）\ leq \ min_ {0 \ leqleqα\ leq leq 1} \ left \ | | αT^* t +（1-α）tt^* \ right \ |，\ |，其中$ w（t）$是$ t的数值半径。作为应用程序，我们估计复杂的一元多项式的零的界限。
New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space $\mathcal{H}$ are given. In particular, it is established that if $T$ is a bounded linear operator on a Hilbert space $\mathcal{H}$ then \[ w^2(T)\leq \min_{0\leq α\leq 1} \left \| αT^*T +(1-α)TT^* \right \|,\] where $w(T)$ is the numerical radius of $T.$ The inequalities obtained here are non-trivial improvement of the well-known numerical radius inequalities. As an application we estimate bounds for the zeros of a complex monic polynomial.
