论文标题
有关保存运营商订单的更多信息
More About Operator Order Preserving
论文作者
论文摘要
众所周知，增加的功能并不能保留运营商的顺序。也不降低功能反向操作员订单。但是，算子单调增加或算子单调减小的功能。在本文中，我们采用凸方法来讨论保存或对话的操作员订单。作为更一般结果的很容易结果，我们发现非负常量$γ$和$ψ$，使得$ a \ leq b $表示$ f（b）\ leq f（a）+γ{\ bf {\ bf {1}}} _ { f（b）+ψ{\ bf {1}} _ {\ Mathcal {h}}，$$用于Hilbert Space $ \ Mathcal $ \ Mathcal {h} $ in Identity Operation $ a，带身份操作员的$ a，b $ a，b $ a，b $包含$ a $和$ b $的光谱。将讨论这些结果与现有文献的联系，并将通过一些示例来强调其意义。
It is well known that increasing functions do not preserve operator order in general; nor do decreasing functions reverse operator order. However, operator monotone increasing or operator monotone decreasing do. In this article, we employ a convex approach to discuss operator order preserving or conversing. As an easy consequence of more general results, we find non-negative constants $γ$ and $ψ$ such that $A\leq B$ implies $$f(B)\leq f(A)+γ{\bf{1}}_{\mathcal{H}}\;~{\text{and}}~\;f(A)\leq f(B)+ψ{\bf{1}}_{\mathcal{H}},$$ for the self adjoint operators $A,B$ on a Hilbert space $\mathcal{H}$ with identity operator ${\bf{1}}_{\mathcal{H}}$ and for the convex function $f$ whose domain contains the spectra of both $A$ and $B$. The connection of these results to the existing literature will be discussed and the significance will be emphasized by some examples.
