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Set-Valued Analysis

, Volume 9, Issue 1–2, pp 35–47 | Cite as

Some Generic Results on Nonattaining Functionals

  • Jonathan Borwein
  • Ivaylo Kortezov
Article

Abstract

We prove that (a) in a reflexive space, for any linearly bounded but unbounded closed convex subset the nonsupport functionals are a dense Gδ subset of the polar set, and (b) any nonsemicoercive proper convex lsc [weak*-lsc] function in a [dual] Banach space has a generic [dense Gδ] 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.

Baire category coercivity non-attaining functionals convex functions 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Jonathan Borwein
    • 1
  • Ivaylo Kortezov
    • 1
  1. 1.CECMSimon Fraser UniversityBurnabyCanada

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