Tensor products of operator systems
Tensor products of operator systems
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DOI：
10.1016/j.jfa.2011.03.014
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发表时间：
2009-10
影响因子：
1.7
通讯作者：
A. Kavruk;V. Paulsen;I. Todorov;M. Tomforde
中科院分区：
文献类型：
--
作者：
A. Kavruk;V. Paulsen;I. Todorov;M. Tomforde
本文的目的是为系统地研究算子系统的张量积奠定基础。在给出这一范畴中张量积的公理定义之后，我们详细地研究了张量积的几个特殊例子，包括极小张量积、极大张量积、极大交换张量积、极大内射张量积和一些非对称张量积。我们用它们的普适性质刻画了这些张量积，并给出了它们的正锥的描述。我们还刻画了由算子空间到算子系统的某种典范包含所诱导的算子空间的相应张量积。我们研究了张量积的核性概念，这些概念在C⁎-代数范畴上退化为经典概念。我们证明了一个算子系统S，它不完全序同构于一个C⁎-代数，但对每个C⁎-代数A，S和A的最小张量积和极大张量积是相等的.
The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular examples of tensor products, including a minimal, maximal, maximal commuting, maximal injective and some asymmetric tensor products. We characterize these tensor products in terms of their universal properties and give descriptions of their positive cones. We also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system. We examine notions of nuclearity for our tensor products which, on the category of C⁎-algebras, reduce to the classical notion. We exhibit an operator system S which is not completely order isomorphic to a C⁎-algebra yet has the property that for every C⁎-algebra A, the minimal and maximal tensor product of S and A are equal.