Journal of Convex Analysis 13 (2006), No. 3, 561--586
Copyright Heldermann Verlag 2006
Maximal Monotonicity via Convex Analysis
Jonathan Borwein
Faculty of Computer Science, Dalhousie University, Halifax, N.S., Canada B3H 1W5
jborwein@cs.dal.ca
In his "23 Mathematische Probleme" lecture to the Paris International Congress in 1900, David Hilbert wrote "Besides it is an error to believe that rigor in the proof is the enemy of simplicity."
In this spirit, we use simple convex analytic methods, relying on an ingenious function due to Simon Fitzpatrick, to provide a concise proof of the maximality of the sum of two maximal monotone operators on reflexive Banach space under standard transversality conditions. Various other surjectivity, convexity and local boundedness results are likewise established.
Keywords: Monotone operators, convex analysis, sandwich theorem, Fenchel duality, sum theorem.
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