论文标题
在Matrix Cauchy-Schwarz上不平等
On the matrix Cauchy-Schwarz inequality
论文作者
论文摘要
这项工作的主要目的是介绍凯奇·史克瓦兹（Cauchy-Schwarz）类型的新矩阵不平等。特别是，我们研究了所谓的LIEB功能，其定义是Cauchy-Schwarz样不平等的伞，然后我们考虑了混合的Cauchy-Schwarz不平等。后一种不平等在获得其他几种基质不等式方面具有影响力，包括数值半径和标准结果。在许多其他结果中，我们表明\ [\ left \ | t \ right \ | \ le \ frac {1} {4} \ left（\ left \ | \ | \ weled | t \ t \ right |+\ weled | {{t}^{*}} \ right |+2 \ mathfrak rtfrak rt \ rt \ rt \ right \ |+|+|+|+| weft \ | weft | weft | weft | weft | \ right | -2 \ mathfrak rt \ right \ |。
The main goal of this work is to present new matrix inequalities of the Cauchy-Schwarz type. In particular, we investigate the so-called Lieb functions, whose definition came as an umbrella of Cauchy-Schwarz-like inequalities, then we consider the mixed Cauchy-Schwarz inequality. This latter inequality has been influential in obtaining several other matrix inequalities, including numerical radius and norm results. Among many other results, we show that \[\left\| T \right\|\le \frac{1}{4}\left( \left\| \left| T \right|+\left| {{T}^{*}} \right|+2\mathfrak RT \right\|+\left\| \left| T \right|+\left| {{T}^{*}} \right|-2\mathfrak RT \right\| \right),\] where $\mathfrak RT$ is the real part of $T$.
