Weakly Almost Periodic of C-Semigroup

In this paper, weakly almost periodic of C-semigroup is studied, Let u(·) is almost-orbit of a bounded C-semigroup on a Banach space X, assuming that u(·) has weakly relatively compact range in X, We obtain that Cu(·) is weakly almost periodic. In particular, in the case that X is reflexive Banach space,we show the same concusion without the assumption of condition that is weakly relatively compact in X is unnecessary for the same concusion. Accordingly we have weakly almost periodic of point in a bounded C-semigroup.