A New Approach to Operator Spaces
A New Approach to Operator Spaces
复制标题
操作员空间的新方法
DOI：
--
复制
发表时间：
1991
期刊：
影响因子：
--
通讯作者：
Z. Ruan
中科院分区：
文献类型：
--
作者：
E. Effros;Z. Ruan
作者以前观察到两个算子空间之间的完全有界映射空间可以实现为算子空间。特别地，在适当的矩阵范数下，算子空间V的对偶与线性算子空间完全等距。这种对偶方法使人们能够制定新的类似物的Banach空间的概念和结果。特别地，存在Banach空间投射张量积的算子空间版本<$μ，其满足期望的函子性质。与Banach空间一样，给定一个算子空间V，函子W|-> V <$μ W保持包含当且仅当是内射算子空间。
Abstract The authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space. In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators. This approach to duality enables one to formulate new analogues of Banach space concepts and results. In particular, there is an operator space version ⊗μ of the Banach space projective tensor product , which satisfies the expected functorial properties. As is the case for Banach spaces, given an operator space V, the functor W |—> V ⊗μ W preserves inclusions if and only if is an injective operator space.