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工作。这项工作将包括：(I)与Banach空间理论有关的算子空间理论，(Ii)局部紧群G的余作用与von Neumann代数和C*-代数上的完全压缩A(G)-模作用之间的内在联系，(Iii)群胚C*-代数的次对角代数，(Iv)对偶算子代数的抽象矩阵范数刻画。C*代数的概念是空间上的一族线性变换的概念的抽象。这些变换也可以被认为在空间的状态中具有值，而负责符号*的这个族的性质是，代数是由在这些状态中的值为实数的变换生成的。这些物体自然而然地出现在数学和物理的许多分支中，这使得研究它们变得重要。

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.