Banach SSD spaces and classes of monotone sets

In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D), type (NI) and strongly representable are equivalent concepts and, consequently, that the known properties of strongly representable sets follow from known properties of sets of type (ED).Comment: 32 page

Quadrivariate existence theorems and strong representability

In this paper, we give conditions under which we can compute the conjugate of a convex function on the product of two Frechet spaces defined in terms of another convex function on the product of two (possibly different) Frechet spaces. We use this result to give simple proofs of some (both old and new) results for Banach spaces, and deduce some (both old and new) stability results for strongly representable multifunctions. We take as our starting point a result on closed convex cones in the product of two Frechet spaces.Comment: 17 pages. Plain TeX (TeXshop

GOSSEZ'S SKEW LINEAR MAP AND ITS PATHOLOGICAL MAXIMALLY MONOTONE MULTIFUNCTIONS

In this note, we give a generalization of Gossez's example of a maximally monotone multifunction such that the closure of its range is not convex, using more elementary techniques than in Gossez's original papers. We also discuss some new properties of Gossez's skew linear operator and its adjoint. While most of this paper uses elementary functional analysis, we correlate our results with those obtained by using the Stone-Cech compactification of the integers.Comment: 8 page