Calculus Rules for Maximal Monotone Operators in General Banach Spaces

The goal of this article is to provide characterizations of monotonicity and maximality via new properties of the Fitzpatrick function associated with a multi-valued operator. Several calculus rules for maximal monotone operators in non-reflexive Banach space settings are presented. In particular positive answers to Rockafellar's conjecture on the maximality of the sum and the chain rule in the linear case are given.