On the range of a coercive maximal monotone operator in a nonreflexive Banach space
Jean–Pierre Gossez · Proceedings of the American Mathematical Society · 1972
It is shown that the range of a coercive everywhere defined maximal monotone operator from a (nonreflexive) Banach space into its dual is dense for the w e a k ∗ \mathrm {weak}^* topology but not necessarily for the norm topology.