TY - JOUR

T1 - New results on q-positivity

AU - García Ramos, Y.

AU - Martínez-Legaz, J. E.

AU - Simons, S.

PY - 2012/7/18

Y1 - 2012/7/18

N2 - 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.

AB - 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.

KW - Lipschitz mappings

KW - Monotonicity

KW - Symmetrically self-dual Banach spaces

KW - Symmetrically self-dual spaces

KW - q-Positive sets

KW - Lipschitz mappings

KW - Monotonicity

KW - Symmetrically self-dual Banach spaces

KW - Symmetrically self-dual spaces

KW - q-Positive sets

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84867048210&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84867048210&origin=inward

U2 - 10.1007/s11117-012-0191-7

DO - 10.1007/s11117-012-0191-7

M3 - Article in a journal

VL - 16

SP - 543

EP - 563

JO - Positivity

JF - Positivity

SN - 1385-1292

IS - 3

ER -