  Maximal monotone operators on a Banach space into its dual can be represented
by convex functions bounded below by the duality product. It is natural to ask
under which conditions a convex function represents a maximal monotone
operator. A satisfactory answer, in the context of reflexive Banach spaces, has
been obtained some years ago. Recently, a partial result on non-reflexive
Banach spaces was obtained.
  In this work we study some others conditions which guarantee that a convex
function represents a maximal monotone operator in non-reflexive Banach spaces.
