$A_{0}(K)$ -空间的量子化
Quantization of $A_{0}(K)$-Spaces
摘要：
本文研究了$L^1$ -矩阵凸集$\{K_{n}\}$在$*$ -局部凸空间中的性质，证明了对于一个适当的$L^1$ -矩阵凸集$\{K_{n}\}$，每个C-$^*$ -序算子空间都是完备等距的，完全同构于$\{A_{0}(K_{n}, M_{n}(V))\}$.进一步，我们将紧凸集的正则嵌入推广到$L^{1}$ -矩阵凸集的$L^{1}$ -正则嵌入.利用$L^{1}$ -凸集的$L^{1}$ -正则嵌入，得到了$A_{0}(K_{n}, M_{n}(V))$是抽象算子系统的条件.
英文摘要：
In this paper, we study $L^1$-matrix convex sets $\{K_{n}\}$ in $*$-locally convex spaces and show that every C$^*$-ordered operator space is complete isometrically, completely isomorphic to $\{A_{0}(K_{n}, M_{n}(V))\}$ for a suitable $L^1$-matrix convex set $\{K_{n}\}$. Further, we generalize the notion of regular embedding of a compact convex set to $L^{1}$-regular embedding of $L^{1}$-matrix convex set. Using $L^{1}$-regular embedding of $L^{1}$-convex set, we find conditions under which $A_{0}(K_{n}, M_{n}(V))$ is an abstract operator system.
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