Topologies of pointwise convergence on families of extremal points and weak compactness

Tweddle, Ian

doi:10.1090/S0002-9939-1982-0663872-0

Topologies of pointwise convergence on families of extremal points and weak compactness
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Proc. Amer. Math. Soc. 86 (1982), 85-86 Request permission

Abstract:

Bourgain and Talagrand showed that a bounded subset of a Banach space is weakly relatively compact provided it is relatively countably compact for the topology of pointwise convergence on the extremal points of the closed unit ball in the dual space. We give a version of this result for quasi-complete locally convex spaces. We also consider situations where the completeness or boundedness assumptions may be relaxed.

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