Some Generic Results on Non-attaining Functionals

Borwein, Jonathan M. and Kortezov, Ivaylo (2001) Some Generic Results on Non-attaining Functionals. Special Issue of Set-valued Analysis on Well-posedness and Stability of Optimization Problems, 9 . pp. 35-47.

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      We prove that (a) in a reflexive space, for any linearly bounded but unbounded closed convex subset the non-support functionals are a dense $G_\delta$ subset of the polar set, and (b) any non-semicoercive proper convex lsc [weak$^*$-lsc] function in a [dual] Banach space has a generic [dense $G_\delta$] set of $L^\infty$-perturbations which do not attain their infimum. We also characterize the proper convex functions that have inf-nonattaining $L^\infty$-perturbations.This results also in a criterion for reflexivity.

      Item Type: Article
      Additional Information: pubdom FALSE
      Subjects: 46-xx Functional analysis > 46Axx Topological linear spaces and related structures
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 13 Jan 2015 12:16

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