Structure in Operator Spaces and Applications

首席研究员David P. Blecher正在进行三条主要的研究路线，主要围绕“非交换线性分析”中的一些最关键的问题，特别是在“算子空间”这个新的但具有开创性的领域。这些线是：1)算子空间的完全等距理论，特别是有用的“非交换Choquet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。该项目还包括集中关注上述技术的各种应用。21世纪数学的一个主要趋势是“非交换”或“量子化”现象，这在很大程度上受到物理学的启发。这种推动力已渗透到数学的大多数分支中。在称为泛函分析的广阔领域中，这种趋势以“算子空间”的名义出现。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和适当的工具来解决“非交换数学”中希尔伯特空间上算子空间的问题。在这个项目中，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）正在研究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.