New results on q-positivity
Simons, S. (University of California)
Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)
García Ramos, Yboon (Centro de Investigación de la Universidad del Pacífico)

Data:	2012
Resum:	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.
Ajuts:	Ministerio de Economía y Competitividad MTM2011-29064-C03-01
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Q-positive sets ; Symmetrically self-dual spaces ; Monotonicity ; Symmetrically self-dual Banach spaces ; Lipschitz mappings
Publicat a:	Positivity, Vol.16, Núm.3, p. 543-563 (2012) , ISSN 1572-9281

DOI: 10.1007/s11117-012-0191-7

Postprint 21 p, 273.6 KB

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