
Journal of Convex Analysis 14 (2007), No. 2, 297317 Copyright Heldermann Verlag 2007 Positive Sets and Monotone Sets Stephen Simons Dept. of Mathematics, University of California, Santa Barbara, CA 931063080, U.S.A. simons@math.ucsb.edu We show how convex analysis can be applied to the theory of sets that are "positive" with respect to a continuous quadratic form on a Banach space. Monotone sets can be considered as a special case of positive sets, and we show how our results lead to very efficient proofs of a number of results on monotone sets. One of the key techniques that we use is a generalization of the Fitzpatrick function from monotone set theory to an analogous function for positive sets. [ Fulltextpdf (190 KB)] for subscribers only. 