RELATIVELY WEAKLY OPEN SETS IN CLOSED BALLS OF C^*-ALGEBRAS

Let A be an infinite-dimensional C^* -algebra. It is proved that every nonempty relatively weakly open subset of the closed unit ball B_A of A has diameter equal to 2. This implies that B_A is not dentable, and that there is not any point of continuity for the identity mapping (B_A, weak) - (B_A, norm) .