by Andrei Verona & Maria E. Verona
 
 
The purpose of this paper is to introduce a class of maximal monotone operators on Banach spaces that contains all maximal monotone operators on reflexive spaces, all subdifferential operators of proper lower semicontinuous convex functions, and, more generally, all maximal monotone operators that verify the simplest possible sum theorem. Dually strongly maximal monotone operators are also contained in this class. We shall prove that if T is an operator in this class then (i) the norm closure of dom(T) its domain is convex, (ii) the interior of the convex hull of the dom(T) is exactly the set of all points of  the closure of the dom(T) at which T is locally bounded, and (iii) T is maximal monotone locally, as well as other results.