Both of the following theorems are referred to as the Krein-Smulian Theorem.
Krein-Smulian Theorem:[2] — Let be a
Banach space and a weakly compact subset of (that is, is compact when is endowed with the
weak topology). Then the closed convex hull of in is weakly compact.
Krein-Smulian Theorem[2] — Let be a
Banach space and a convex subset of the continuous dual space of . If for all is
weak-* closed in then is weak-* closed.
See also
KreinâMilman theorem â On when a space equals the closed convex hull of its extreme points
Weak-* topology â Mathematical termPages displaying short descriptions of redirect targets