The Grothendieck-Pietsch and Dvoretzky-Rogers Theorems for Operator Spaces
The Grothendieck-Pietsch and Dvoretzky-Rogers Theorems for Operator Spaces
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DOI：
10.1006/jfan.1994.1075
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发表时间：
1994-06
影响因子：
1.7
通讯作者：
E. Effros;Z. Ruan
中科院分区：
文献类型：
--
作者：
E. Effros;Z. Ruan
算子空间是Hilbert空间上有界算子的线性空间。遵循海森伯格关于算符提供函数的量子类比的原理，人们可能会认为，许多经典泛函分析都会有算符空间类比。从Arveson发现类似Hahn-Banach定理[1，2-4，10-13，18]开始，许多论文都在探讨这一观点。Grothendieck是第一个使用映射空间来研究Banach空间的人(见[15，16])，这仍然是该学科中最强大的技术之一。根据本文的结果，现在很明显，Grothendieck程序的主要组成部分在算子空间的上下文中是有意义的。下表总结了这在多大程度上
An operator space is a linear space of bounded operators on a Hilbert space. Following Heisenberg's principle that operators provide the quantum analogue of functions, one might expect that much of classical functional analysis would have operator space analogues. This idea has been pursued in a number of papers, beginning with Arveson's discovery of an analogue of the Hahn-Banach Theorem [1, 2–4, 10–13, 18]. Grothendieck was the first to use mapping spaces to study Banach spaces (see [15, 16]), and this remains one of the most powerful techniques in that subject. With the results of this paper, it is now evident that major components of Grothendieck's program make sense in the context of operator spaces. The following table summarizes the extent to which this is