论文标题
是双空间的非积极操作员系统
Non-unital operator systems that are dual spaces
论文作者
论文摘要
我们将对$ \ MATHCAL {L}（H）$的任意自我预科弱$^*$ - 封闭子空间进行抽象表征（配备了诱导的矩阵标准，诱导的矩阵锥和诱导的弱$^*$ - 拓扑）。为此，我们获得了$^*$ - 运算符的Bonsall结果的矩阵类似物，配备了封闭矩阵锥体。在途中，我们观察到，对于配备矩阵锥的$^*$ - 向量$ x $（尤其是当$ x $是操作员系统或操作员系统的双空间时），线性映射$ ϕ：x \ to m_n $是完全积极的，并且仅当线性函数$ [x______ {i，j} i，j} i，j} i，j} i，j} \ sum_ {i，j = 1}^n ϕ（x_ {i，j}）_ {i，j} $ on $ m_n（x）$是正面的。
We will give an abstract characterization of an arbitrary self-adjoint weak$^*$-closed subspace of $\mathcal{L}(H)$ (equipped with the induced matrix norm, the induced matrix cone and the induced weak$^*$-topology). In order to do this, we obtain a matrix analogues of a result of Bonsall for $^*$-operator spaces equipped with closed matrix cones. On our way, we observe that for a $^*$-vector $X$ equipped with a matrix cone (in particular, when $X$ is an operator system or the dual space of an operator system), a linear map $ϕ:X\to M_n$ is completely positive if and only if linear functional $[x_{i,j}]_{i,j}\mapsto \sum_{i,j=1}^n ϕ(x_{i,j})_{i,j}$ on $M_n(X)$ is positive.
