A classical problem in functional analysis has been to give a geometric characterization of reflexivity for a Banach space. The first result of this type was D.P. Milman’s [Mil] and B.J. Pettis’ [P] theorem that a uniformly convex space is reflexive. While perhaps considered elementary today it illustrated how a geometric property can be responsible for a topological property. Of course a Banac...

We study various properties of convex functions and their connections to the structure of the spaces on which they are deened. In particular, it is shown boundedness properties of convex functions on various bornologies are related to sequential convergence in dual topologies. Convex functions whose subdiierentials have range with nonconvex interior are constructed on nonreeexive spaces, and we...

This paper presents the proof of the relative Oka-Grauert principle for holomorphic submersions over 1-convex spaces using conic neighbourhoods of holomorphic sections over 1-convex spaces. A proof of a version of Cartan’s Theorem A for 1-convex spaces is also given.