Some Generic Results on Nonattaining Functionals
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We prove that (a) in a reflexive space, for any linearly bounded but unbounded closed convex subset the nonsupport functionals are a dense G δ subset of the polar set, and (b) any nonsemicoercive proper convex lsc [weak*-lsc] function in a [dual] Banach space has a generic [dense G δ] set of L ∞-perturbations which do not attain their infimum. We also characterize the proper convex functions that have inf-nonattaining L ∞-perturbations. This results also in a criterion for reflexivity.
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- Some Generic Results on Nonattaining Functionals
Volume 9, Issue 1-2 , pp 35-47
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- Baire category
- non-attaining functionals
- convex functions