Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type

Abstract

We show that every maximally monotone operator of Fitzpatrick-Phelps type defined on a real Banach space must be of dense type. This provides an affirmative answer to a question posed by Stephen Simons in 2001 and implies that various important notions of monotonicity coincide.Comment: 8 page