Structure in Operator Spaces and Applications

操作空间和应用程序的结构

• 批准号: 0400731
• 负责人: David Blecher
• 金额: --
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-01 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0400731&HistoricalAwards=false
• 关键词: Structure; Operator; Spaces; Applications

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.

首席研究员David P. Blecher正在追求三个主要研究线，重点是“非交通性线性分析”中一些最关键的问题，尤其是在新的但开创性的“操作员空间”的开创性领域。 这些线是1）操作员空间的完全等距理论，尤其是有用的“非交易性choquet理论”的持续发展，2）操作员空间的完全同构理论，3）操作者代数的一般理论。 该项目还包括对上述技术的不同应用的密切关注。 21世纪数学的主要趋势主要受到物理的启发，是朝向“非交通”或“量化”现象。 这种推力已经渗透到大多数数学分支。 在被称为功能分析的广阔领域，这种趋势以“操作员空间”的名义出现。 经营者空间的年轻但开创性领域的主要目的是提供新的且适当的工具，以解决有关Hilbert Space上运营商的问题，这些问题是在“非交易性数学”中引起的。 有了这个项目，研究人员（他本身以及该领域的其他几个主要研究人员）正在攻击该主题中最重要，最关键的问题。 这项工作将提供主要的新工具，该工具将在几个不同的领域中应用：线性分析，操作员理论，操作员代数和量子物理学。