AI 中文总结
该文研究二次对偶与$C^*$-代数等距的复Banach空间相关的弱紧算子，证明伴随算子保持特定端点结构的算子集为一致强端点集，并拓展到全体算子空间的情形。
AI 中文摘要
设$\Omega$为紧Hausdorff空间，$X$为复Banach空间且其二次对偶$X^{**}$与一个$C^*$-代数等距同构。记$\mathcal{W}(X^*, C(\Omega))$为弱紧算子空间。本文证明：$\mathcal{W}(X^*, C(\Omega))$中满足$T^*$将$C(\Omega)^*$单位球的线性端点映射到$X^{**}$的$C^*$-端点的算子全体构成一致强端点集。我们还探究了当$X^{**}$与某Banach空间上的全体算子空间等距同构时的上述现象。
英文摘要
Let $Ω$ be a compact Hausdorff space and $X$ be a complex Banach space such that $X^{**}$ is isometric to a $C^*$-algebra. Let $\mathcal{W}(X^*, C(Ω))$ denote the space of weakly compact operators. In this article, we show that the collection of operators $T$ in $\mathcal{W}(X^*, C(Ω))$ such that $T^*$ maps linear extreme points of the unit ball of $C(Ω)^*$ to $C^*$-extreme points of $X^{**}$ is a uniformly strongly extreme set. We also investigate this phenomenon when $X^{**}$ is isometric to a space of all operators on a Banach space.
Comments11 pages. Comments are welcome
