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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2014

Generic Hahn–Banach results

Résumé

Given f:X→R∪{+∞}f:X→R∪{+∞} a convex and lower semi-continuous function defined on a reflexive Banach space X, and L, a closed linear manifold of X over which f takes at least a real value, the aim of this note is to prove the following Baire category result: in the Euclidean setting, the set of affine functions dominated by f on L for which there is no dominated extension to X is always of first Baire category, but this set can be as large as a residual set, provided that X is a reflexive Banach space of infinite dimension.
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Dates et versions

hal-01118526 , version 1 (16-07-2015)

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Emil Ernst, Michel Volle. Generic Hahn–Banach results. Journal of Mathematical Analysis and Applications, 2014, 420 (1), pp.137-144. ⟨10.1016/j.jmaa.2014.05.075⟩. ⟨hal-01118526⟩
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