An extension of the Krein-Šmulian Theorem
An extension of the Krein-Šmulian Theorem
Let X be a Banach space, u\in X^{**} and K, Z two subsets of X^{**} . Denote by d(u,Z) and d(K,Z) the distances to Z from the point u and from the subset K respectively. The Krein-Šmulian Theorem asserts that the closed convex hull of a weakly compact subset of …