Hahn—Banach and Banach—Steinhaus theorems for convex processes

Our goal in this paper is to prove versions of the Hahn—Banach and Banach—Steinhaus theorems for convex processes. For the first theorem, we prove that each real convex process corresponds to a sublinear or superlinear functional and then we extend these. For the second theorem, we previously show that there is a seminorm naturally associated to the class of lower semi-continuous convex processes.