Operator spaces and harmonic analysis

算子空间和调和分析

• 批准号: 312515-2010
• 负责人: Spronk, Nicolaas
• 金额: $ 1.75万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=526552
• 关键词: Operator; spaces; harmonic; analysis

Groups are amongst the most natural mathematical objects, developed to model symmetries. Infinite groups often have unruly algebraic behavior, which can frequently be tamed by examining their spatial behavior, i.e. using topology. Representation theory is is an important tool for understanding these topological groups. I am interested in studying particular mathematical objects, certain Banach algebras, which are associated with these representations. These algebras, coming from representation theory, are very closely related to operators (the natural framework in which representations are understood), and this connection allows for non-trivial spatial structures to be viewed in these algebras, which we hence call operator space structures. This is non-commutative harmonic analysis.

群是最自然的数学对象之一，是用来模拟对称性的。无限群通常具有难以驾驭的代数行为，这通常可以通过检查它们的空间行为来驯服，即使用拓扑学。表示论是理解这些拓扑群的重要工具。我对研究特定的数学对象，某些与这些表示有关的Banach代数很感兴趣。这些代数源于表示理论，与算子(理解表示的自然框架)密切相关，这种联系允许在这些代数中看到非平凡的空间结构，因此我们称之为算子空间结构。这是非对易调和分析。