Structure in Operator Spaces and Applications

首席研究员David P.Blecher正在进行三条主线的研究，重点围绕着“非对易线性分析”中的一些最关键的问题，特别是在新的但具有开创性的“算子空间”领域。这些线条是：1)算子空间的完全等距理论，尤其是一个有用的‘非对易Choket理论’的继续发展；2)算子空间的完全同构理论；3)算子代数的一般理论。该项目还包括对上述技术的各种应用的密集关注。在主要受物理学启发的21世纪，数学的一个主要趋势是走向“非对易”或“量子化”现象。这一推动力已经渗透到数学的大多数分支。在被称为泛函分析的广大领域中，这一趋势在“算符空间”的名义下明显地出现了。算子空间这个年轻但具有开创性的领域的主要目的是提供新的适当的工具来解决在非交换数学中出现的关于Hilbert空间上的算子空间的问题。通过这个项目，这位研究人员(独自一人，并与该领域的其他几位主要研究人员一起)正在解决该学科中几个最重要和最关键的问题。这项工作将提供主要的新工具，这些工具将应用于几个不同的领域：线性分析、算符理论、算符代数和量子物理。

The principal investigator, David P. Blecher, is pursuing three main lines of research, focused around some of the most critical problems in `noncommutative linear analysis', and in particular in the new but seminal field of `operator spaces'. These lines are 1)the completely isometric theory of operator spaces, most particularly a continuing development of a useful `noncommutative Choquet theory', 2) the completely isomorphic theory of operator spaces, 3) the general theory of operator algebras. This project also includes an intensive focus on diverse applications of the above technology. A major trend in mathematics in the 21st century, inspired largely by physics, is toward `noncommutative' or `quantized' phenomena. This thrust has permeated most branches of mathematics. In the vast area known as functional analysis, this trend has appeared notably under the name of `operator spaces'. The main purpose of the young but seminal field of operator spaces, is to provide new and appropriate tools to solve problems concerning spaces of operators on Hilbert space arising in `noncommutative mathematics'. With this project, the investigator (on his own, and together with several of the other major researchers in this area) is attacking several of the most important and critical problems in the subject. This work will provide major new tools, which will have applications to several diverse fields: linear analysis, operator theory, operator algebras, and quantum physics.