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.
