Structure in Operator Spaces and Applications

首席研究员，大卫P. Blecher，是追求三个主要的研究路线，集中在一些最关键的问题，在“非交换线性分析”，特别是在新的，但开创性的领域“运营商空间”。 这些线是1）完全等距理论的经营者空间，最特别是一个继续发展的一个有用的“非交换Choquet理论”，2）完全同构理论的经营者空间，3）一般理论的经营者代数。 该项目还包括对上述技术的各种应用的集中关注。 21世纪数学的一个主要趋势，很大程度上受到物理学的启发，是朝向“非交换”或“量子化”现象。 这一主旨已渗透到数学的大多数分支。 在被称为功能分析的广阔领域，这一趋势以“操作员空间”的名义出现。 算子空间这一年轻但具有开创性的领域的主要目的，是提供新的和适当的工具来解决有关希尔伯特空间上的算子空间在“非对易代数学”中出现的问题。 通过这个项目，研究者（独自一人，并与该领域的其他几位主要研究人员一起）正在解决该主题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，这将有应用到几个不同的领域：线性分析，算子理论，算子代数和量子物理。

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.