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

阮教授将继续他在算子空间和算子代数方面的研究。这项工作将包括以下方面的研究：(i)与Banach空间理论相关的算子空间理论，（ii）局部紧群G与完全压缩A(G)-模作用在von Neumann代数和C*-代数上的内在关系，（iii）群C*-代数的次对角代数，（iv）对偶算子代数的抽象矩阵范数表征。C*代数的概念是对空间上一系列线性变换的抽象。这些变换也可以被认为是在空间的状态中有值，这个族的性质是负责符号*的是代数是由这些状态中的值是实数的变换生成的。这些对象在数学和物理的许多分支中自然出现的事实，使它们成为研究的重要对象。

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.