Global and internal structure of operator algebras

算子代数的全局和内部结构

• 批准号: RGPIN-2015-06205
• 负责人: Marcoux, Laurent
• 金额: $ 1.02万
• 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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=590908
• 关键词: Global; internal; structure; 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) 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. For example, if we compose two rotations, we simply obtain another rotation. If we add two translations, we obtain another translation. Such collections are referred to as algebras.

我的研究属于纯数学领域，称为算子理论和算子代数。 非常宽松地说，这是一个研究线性变换集的领域，其中三维空间 R^3 中的旋转、反射和膨胀只是三个例子。 我的兴趣是研究 R^3 的无限维类似物（称为希尔伯特空间）中的线性变换。 其中一些线性变换（或运算符）集合具有某些代数属性，允许我们缩放成员、组成两个变换或添加两个变换，但仍然保留在集合中。 例如，如果我们组合两个旋转，我们只需获得另一个旋转。 如果我们添加两个翻译，我们会得到另一个翻译。 这样的集合称为代数。