The present note deals with operator Hilbert systems, which are quantizations of unital cones in Hilbert spaces. One central result of the note is that the Pisier operator Hilbert space is an operator system whose quantum cone of positive elements is described in terms of the quantum ball of the relevant conjugate Hilbert space. Finally, we obtain a solution to the problem of Paulsen, Todorov and Tomforde on separable morphisms between operator systems and characterize minmax- completely positive maps between Archimedean order unit spaces.

中文翻译：

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运营商希尔伯特系统

本说明涉及算子希尔伯特系统，它是希尔伯特空间中单位锥的量化。该注释的一个主要结果是，Pisier算符希尔伯特空间是一个算子系统，其正元素的量子锥是根据相关共轭希尔伯特空间的量子球描述的。最后，我们获得了关于Paulsen，Todorov和Tomforde在算子系统之间可分态射影上的问题的解决方案，并描述了Archimedean阶单位空间之间的minmax-完全正图。