Abstract
We show that in certain non-locally convex Orlicz function spacesL ϕ with trivial dual every compact convex set is locally convex and hence the Krein-Milman theorem holds. This complements the example constructed by Roberts of a compact convex set without extreme points inL p (0<p<1) and answers a question raised by Shapiro.
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Kalton, N.J. AnF-space with trivial dual where the Krein-Milman theorem holds. Israel J. Math. 36, 41–49 (1980). https://doi.org/10.1007/BF02761229
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DOI: https://doi.org/10.1007/BF02761229