论文标题
精致的亨氏经营者的不平等和规范不平等现象
Refined Heinz operator inequalities and norm inequalities
论文作者
论文摘要
在本文中，我们研究了亨氏和埃尔米特 - 哈达玛德的不平等现象。我们得出了涉及单位不变规范的这些不平等的整个改进，从而改善了文献所知的一些最新结果。 我们还证明，如果$ a，b，x \ in m_n（\ mathbb {c}）$，这样$ a $ and $ b $是正定确定的，而$ f $是$（0，\ infty）$的操作员单调函数。然后\ begin {equination*} ||| f（a）x-xf（b）||| \ leq \ leq \ max \ {|| f'（a）||，|| || f'（b）|| \} || \} ||| ax-xb ||||。 \ end {等式*}最后，我们获得了亨氏操作员不平等的一系列改进，这是Kittaneh andKrnić证明的。
In this article we study the Heinz and Hermite-Hadamard inequalities. We derive the whole series of refinements of these inequalities involving unitarily invariant norms, which improve some recent results, known from the literature. We also prove that if $A , B, X\in M_n(\mathbb{C})$ such that $A$ and $B$ are positive definite and $f$ is an operator monotone function on $(0,\infty)$. Then \begin{equation*} |||f(A)X-Xf(B)|||\leq \max\{||f'(A)||, ||f'(B)||\} |||AX-XB|||. \end{equation*} Finally we obtain a series of refinements of the Heinz operator inequalities, which were proved by Kittaneh and Krnić.
