论文标题
数值半径的新估计值
New Estimates for the Numerical Radius
论文作者
论文摘要
在本文中，我们介绍了两个希尔伯特太空运营商总和的数值半径的新不平等。这些新的不平等将使我们能够获得一些知名不平等的概括和改进，包括数值半径和规范界限的乘法行为。 在许多其他应用程序中，显示出$ t $是增值性的，则\ [\ frac {1} {\ sqrt {2}}} \ left \ | t \ right \ | \leΩ\ left（t \ right），\]其中$ω\ left（\ cdot \ right）$和$ \ left \ | | \ cdot \ right \ | $分别表示数值半径和常规运算符规范。这种不平等为众所周知的不平等$ \ frac {1} {2} {2} \ | t \ | \ | \ leqω（t）。$提供了相当大的改进。
In this article, we present new inequalities for the numerical radius of the sum of two Hilbert space operators. These new inequalities will enable us to obtain many generalizations and refinements of some well known inequalities, including multiplicative behavior of the numerical radius and norm bounds. Among many other applications, it is shown that if $T$ is accretive-dissipative, then \[\frac{1}{\sqrt{2}}\left\| T \right\|\le ω\left( T \right),\] where $ω\left( \cdot \right)$ and $\left\| \cdot \right\|$ denote the numerical radius and the usual operator norm, respectively. This inequality provides a considerable refinement of the well known inequality $\frac{1}{2}\|T\|\leq ω(T).$
