Dr John Ormerod
Let A be a separable C*-algebra. We show that the discreteness of its spectrum sp(A) is equivalent to the fact that its Banach space dual A* has the weak* fixed point property, and some other properties. Among these are the uniform Kadec-Klee property for A* and coincidence of the weak* and the norm topology on the pure states of A. This is joint work with Gero Fendler (Vienna).