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Incoming links: Goldstine theorem
Weak compactness characterization of reflexivity Created 2026-09-28 Updated 2026-10-05
A Banach space is reflexive if and only if its closed unit ball is compact in the weak topology. One direction applies the Banach-Alaoglu theorem to the unit ball in the bidual; the converse follows because Goldstine theorem makes the canonical image of the unit ball weak-star dense, while weak compactness makes that image weak-star closed.