 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Xxxx XXXX, Pages 000000
S 00029939(XX)00000 2000]Primary 47H05; Secondary 26B25
A NEW PROOF FOR ROCKAFELLAR'S CHARACTERIZATION
OF MAXIMAL MONOTONE OPERATORS
S. SIMONS AND C. Z –
ALINESCU
Abstract. We provide a new and short proof for Rockafellar's characteriza
tion of maximal monotone operators in reflexive Banach spaces based on S.
Fitzpatrick's function and a technique used by R. S. Burachik and B. F. Svaiter
for proving their result on the representation of a maximal monotone operator
by convex functions.
1. The result
Throughout this note (X, #·#) is a reflexive Banach space and X # is its topological
dual space whose dual norm is denoted by #·# # . Then the topological dual of X×X #
is X # ×X, the pairing being given by #(x, x # ), (u # , u)# := #x, u # #+#u, x # # , where, as
usual, #x, u # # := u # (x) for x # X and u # # X # . Let A : X ¶ X # be a multivalued
operator (or multifunction) whose graph gr A := {(x, x # )  x # # A(x)} is nonempty.
Recall that A is monotone if
