Conjugate quasiconvex nonnegative functions

Abstract

A conjugacy operation defined on the complete lattice Q(X) of all nonegative quasiconvex lower semicontinuous functions defined on locally convex space X and vanishing at zero is considered. Properties of this operation and of the lattice Q(X) are outlined. In particular a set of extreme rays of Q(X) which generates this conic lattice by means of the operation 'sup' is described, the connection between summation and the conjugacy operation is established.