Structure and perturbations of operator algebras

算子代数的结构和扰动

• 批准号: 89693-2010
• 负责人: Marcoux, Laurent
• 金额: $ 1.46万
• 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: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508699
• 关键词: Structure; perturbations; operator; algebras

My research is in an area of Pure Mathematics known as Operator Theory and Operator Algebras. Very loosely speaking, this is an area which studies sets of linear transformations, of which rotations, reflections, and dilations in our three-dimensional space $R^3$ are but three examples. My interest is to study linear transformations in the infinite-dimensional analogues of $R^3$ known as Hilbert spaces. Some of these collections of linear transformations (or operators, as they are also known) possess certain algebraic properties, allowing us to scale the members, to compose two transformations, or add two transformations, and yet still remain in the collection.

我的研究是在纯数学领域，称为操作者理论和操作员代数。非常宽松地说，这是一个研究一组线性变换的领域，其中三维空间中的旋转，反射和扩张$ r^3 $不过是三个例子。 我的兴趣是研究$ r^3 $的无限维度类似物中的线性变换，称为希尔伯特空间。这些线性变换的集合中的一些（或众所周知的运算符）具有某些代数属性，使我们可以扩展成员，构成两个转换或添加两个转换，但仍保留在集合中。