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: 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=521832
• 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被称为算子理论和算子代数。非常松散地说，这是一个研究线性变换集的领域，其中旋转，反射和膨胀在我们的三维空间R^3中只是三个例子。 我的兴趣是研究线性变换在无穷维类似的$R ^3 $被称为希尔伯特空间。这些线性变换（或运算符，因为它们也被称为）的集合中的一些具有某些代数性质，允许我们缩放成员，组合两个变换，或添加两个变换，但仍然保留在集合中。