Krein–Smulian theorem

In mathematics, particularly in functional analysis, the Krein-Smulian theorem can refer to two theorems relating the closed convex hull and compactness in the weak topology.

They are named after Mark Krein and Vitold Shmulyan, who published them in 1940.

be a Banach space and

a weakly compact subset of

is endowed with the weak topology).

Then the closed convex hull of

be a Banach space and

a convex subset of the continuous dual space

is weak-* closed in

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