Mathematical Sciences: Operator Algebras

数学科学：算子代数

• 批准号: 8702982
• 负责人: David Pitts
• 金额: $ 1.93万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-15 至 1990-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702982&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operator; Algebras

Operator algebras is a central discipline in Modern Analysis which has important historical and current applications. It arose in the early decades of this century in connection with establishing a mathematical framework for quantum mechanics. This pioneering work, associated with the names of von Neumann and Murray, and referred to as the noncommutative analog of probability theory and of measure theory, treated selfadjoint algebras of operators. In recent years, again in connection with applications in physics as well as in engineering and operator theory, mathematicians have turned their attention to the theory of non-selfadjoint operator algebras. This study is in its infancy, and the structure theory of such algebras is being intensively investigated. Professor Pitts is a young mathematical analyst whose research career is off to a stunning start. He recently completed his doctoral dissertation on the structure of certain types of non-selfadjoint operator algebras called nest algebras, studying them as subalgebras of von Neumann (selfadjoint) algebras. In this work he obtained several new results on factorization problems and connections with K- theory of these algebras. In the current proposal, Professor Pitts plans to continue his successful research activity by investigating difficult and long outstanding problems concerning similarity and connectedness questions in nest algebras.

算子代数是现代数学的一个中心学科 具有重要历史和当前应用的分析。 它产生于本世纪的前几十年， 建立量子力学的数学框架。 这项开创性的工作，与冯诺依曼的名字联系在一起， 和默里，并被称为非交换模拟的 概率论和测度论，处理自伴的 算子代数 近年来，在与 在物理、工程和操作中的应用 理论，数学家们已经把注意力转向了 非自伴算子代数理论 这项研究在 它的婴儿期，这种代数的结构理论是 正在深入调查。 皮茨教授是一位年轻的数学分析家， 研究生涯有了一个惊人的开端 他最近 完成了他的博士论文的结构 某些类型的非自伴算子代数称为 套代数，研究他们作为子代数的冯诺依曼 （自伴）代数。 在这项工作中，他获得了几个新的 关于因子分解问题和与K- 这些代数的理论。 在目前的情况下，教授 皮茨计划继续他成功的研究活动， 查处长期存在的突出问题 关于nest中的相似性和连通性问题 代数