论文标题
在凯奇 - 史瓦兹（Cauchy-Schwarz）型不平等和应用数字半径不平等
On Cauchy-Schwarz type inequalities and applications to numerical radius inequalities
论文作者
论文摘要
在这项工作中，证明了内部产品空间中的Cauchy-Schwarz的不平等现象。建立了更普遍的加藤不平等现象或所谓的混合施瓦茨不平等现象。还指出了一些著名的数值半径不平等的改进。如这项工作所示，这些改进概括并完善了文献中获得的一些近期和旧结果。除其他外，还证明，如果$ t \ in \ Mathscr {b} \ left（\ Mathscr {h} \ right）$，则\ begin {align*}ω^{2} \ left（t \ weft（t \ right） \ left | T \右|+\左| {t^*} \ right | \ right \ |^2 + \ frac {1} {3}ω\ left（t \ right）\ left \ | \ left | T \右|+\左| {t^*} \ right | \ right \ | \\＆\ le \ frac {1} {6} \ left \ | \ left | t \右|^2+ \左| {t^*} \ right |^2 \ right \ | + \ frac {1} {3}ω\ left（t \ right）\ left \ | \ left | T \右|+\左| {t^*} \ right | \ right \ |，\ end {align*}，它完善了Kittaneh和Moradi在\ cite {km}中获得的最新不平等。
In this work, a refinement of the Cauchy--Schwarz inequality in inner product space is proved. A more general refinement of the Kato's inequality or the so called mixed Schwarz inequality is established. Refinements of some famous numerical radius inequalities are also pointed out. As shown in this work, these refinements generalize and refine some recent and old results obtained in literature. Among others, it is proved that if $T\in\mathscr{B}\left(\mathscr{H}\right)$, then \begin{align*} ω^{2}\left(T\right) &\le \frac{1}{12} \left\| \left| T \right|+\left| {T^* } \right|\right\|^2 + \frac{1}{3} ω\left(T\right)\left\| \left| T \right|+\left| {T^* } \right|\right\| \\ &\le\frac{1}{6} \left\| \left| T \right|^2+ \left| {T^* } \right|^2 \right\| + \frac{1}{3} ω\left(T\right)\left\| \left| T \right|+\left| {T^* } \right|\right\|, \end{align*} which refines the recent inequality obtained by Kittaneh and Moradi in \cite{KM}.
