标题： 算子空间结构与分裂性质 II 显示英文标题

标题： Operator space structures and the split property II

摘要： 建立了可分预对偶的$W^*$- 因子包含$N\subset M$的分裂性质的一个特征，这是通过与任意固定的标准向量$\Om$对应的\cite{B1,B2} $$ \F_2:a\in N\to \D_{M,\Om}^{1/4}a\Om\in L^2(M,\Om) $$ 中所考虑的典型非交换$L^2$嵌入来刻画的，其中涉及$M$。 这一刻画遵循与经典的非交换嵌入相关的类似刻画，即 $L^1$ 嵌入 $$ \F_1:a\in N\to (\cdot\Om,J_{M,\Om}a\Om)\in L^1(M,\Om) $$，这也出现在 \cite{B1,B2} 中并在 \cite{F} 中研究。 量子场论的分裂性质通过相对于非交换嵌入 $\F_i$, $i=1,2$ 的等价条件来刻画，这些嵌入由特权忠实态（例如真空态）的模 Hamiltonian 构造。 上述刻画对于时空弯曲情况下的理论也有用，在这种情况下不存在先验的特权态。 显示英文摘要

摘要： A characterization of the split property for an inclusion $N\subset M$ of $W^*$-factors with separable predual is established in terms of the canonical non-commutative $L^2$ embedding considered in \cite{B1,B2} $$ \F_2:a\in N\to \D_{M,\Om}^{1/4}a\Om\in L^2(M,\Om) $$ associated with an arbitrary fixed standard vector $\Om$ for $M$. This characterization follows an analogous characterization related to the canonical non-commutative $L^1$ embedding $$ \F_1:a\in N\to (\cdot\Om,J_{M,\Om}a\Om)\in L^1(M,\Om) $$ also considered in \cite{B1,B2} and studied in \cite{F}. The split property for a Quantum Field Theory is characterized by equivalent conditions relative to the non-commutative embeddings $\F_i$, $i=1,2$, constructed by the modular Hamiltonian of a privileged faithful state such as e.g. the vacuum state. The above characterization would be also useful for theories on a curved space-time where there exists no a-priori privileged state.