Mathematical Sciences: Operator Spaces, Operator Algebras and Completely Bounded Maps

数学科学：算子空间、算子代数和全有界图

• 批准号: 9102109
• 负责人: Zhong-Jin Ruan
• 金额: $ 3.84万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-05-15 至 1993-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102109&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operator; Spaces; Algebras

Professor Ruan will continue his work on operator spaces and operator algebras. This work will include investigations in (i) the theory of operator spaces in connection with the theory of Banach spaces, (ii) the intrinsic relations between the coactions of locally compact groups G and the completely contractive A(G)- module actions on von Neumann algebras and C*-algebras, (iii) subdiagonal algebras of groupoid C*-algebras, (iv) the abstract matrix norm characterization of dual operator algebras. The notion of a C* algebra is an abstraction of the idea of a family of linear transformations on a space. These transformations can also be thought of as having values in the states of the space, and the property of this family which is responsible for the symbol * is that the algebra is generated by transformations whose values in these states are real numbers. The fact that these objects appear naturally in many branches of mathematics and physics make them important to study.

阮教授将继续他在算子空间方面的工作， 算子代数 这项工作将包括以下方面的调查： 算子空间理论与 Banach空间，（ii）余作用之间的内在关系 局部紧群G和完全压缩群A（G）- von Neumann代数和C ~*-代数上的模作用，（iii） 广群C ~*-代数的次对角代数，（iv）抽象 对偶算子代数的矩阵范数刻画 C* 代数的概念是以下概念的抽象： 空间上的线性变换族。 这些 转换也可以被认为是在 空间的状态，以及这个家庭的属性， 负责符号 * 的是，代数是由 在这些状态下其值为真实的数的变换。 的 事实上，这些物体自然地出现在许多分支中， 数学和物理使它们成为重要的学习内容。