论文标题
数值半径不平等的高级改进
Advanced Refinements of Numerical Radius Inequalities
论文作者
论文摘要
我们证明了希尔伯特空间中线性算子的几个数值半径不平等。除其他不等式外，如果$ a $是复杂的希尔伯特空间上的有界线性运算符，那么\ [ω\ left（a \ right）\ le \ frac {1} {2} {2} \ sqrt {\ sqrt {\ left \ | | {{\ left | a \ right |}^{2}}}+{{{\ left | {{{a}^{*}}} \ right |}^{2}}} \ right \ |+\ \ lest \ | \ left | \右| \ left | {{a}^{*}} \ right |+\ left | {{{a}^{*}}} \ right | \ left | \ right | \ right \ |}，\]其中$ω\ left（a \ right）$，$ \ left \ | \ right \ | $，$ \ left | \右| $是数值半径，通常的运算符标准和$ a $的绝对值。这种不等式提供了由于kittaneh引起的早期数值半径不等式的改进，即，\ [ω\ left（a \ right）\ le \ frac {1} {2} {2} {2} \ left（\ left \ lest \ | a \ | a \ |还讨论了一些相关的不等式。
We prove several numerical radius inequalities for linear operators in Hilbert spaces. It is shown, among other inequalities, that if $A$ is a bounded linear operator on a complex Hilbert space, then \[ω\left( A \right)\le \frac{1}{2}\sqrt{\left\| {{\left| A \right|}^{2}}+{{\left| {{A}^{*}} \right|}^{2}} \right\|+\left\| \left| A \right|\left| {{A}^{*}} \right|+\left| {{A}^{*}} \right|\left| A \right| \right\|},\] where $ω\left( A \right)$, $\left\| A \right\|$, and $\left| A \right|$ are the numerical radius, the usual operator norm, and the absolute value of $A$, respectively. This inequality provides a refinement of an earlier numerical radius inequality due to Kittaneh, namely, \[ω\left( A \right)\le \frac{1}{2}\left( \left\| A \right\|+{{\left\| {{A}^{2}} \right\|}^{\frac{1}{2}}} \right).\] Some related inequalities are also discussed.
