New results on q-positivity

Y. García Ramos, J. E. Martínez-Legaz, S. Simons

Research output: Contribution to journalArticle in a journalpeer-review

3 Scopus citations


In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original bilinear form. The notion of q-positivity generalizes the classical notion of the monotonicity of a subset of a product of a Banach space and its dual. Maximal q-positivity then generalizes maximal monotonicity. We discuss concepts generalizing the representations of monotone sets by convex functions, as well as the number of maximally q -positive extensions of a q-positive set. We also discuss symmetrically self-dual Banach spaces, in which we add a Banach space structure, giving new characterizations of maximal q-positivity. The paper finishes with two new examples.
Original languageEnglish
Pages (from-to)543-563
Number of pages21
Issue number3
StatePublished - 18 Jul 2012


  • Lipschitz mappings
  • Monotonicity
  • Symmetrically self-dual Banach spaces
  • Symmetrically self-dual spaces
  • q-Positive sets


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