Let X be a dual space of a separable Banach space.It is proved that X has w~*-normal structure if X has the property(P~*)there exist an ε<1 and a δ<1 such that whenever a sequence (x_) in the closed unit ball ...Let X be a dual space of a separable Banach space.It is proved that X has w~*-normal structure if X has the property(P~*)there exist an ε<1 and a δ<1 such that whenever a sequence (x_) in the closed unit ball of X with ‖x_n-x_m‖≥ε for all n≠m converges weak- star to x,then ‖x‖≤1-δ.展开更多
文摘Let X be a dual space of a separable Banach space.It is proved that X has w~*-normal structure if X has the property(P~*)there exist an ε<1 and a δ<1 such that whenever a sequence (x_) in the closed unit ball of X with ‖x_n-x_m‖≥ε for all n≠m converges weak- star to x,then ‖x‖≤1-δ.
