A Dual Criterion for Maximal Monotonicity of Composition Operators

In this paper we present a dual criterion for the maximal monotonicity of the composition operator , where is a maximal monotone (set-valued) operator and is a continuous linear map with the adjoint , and are reflexive Banach spaces, and the product notation indicates composition. The dual criterion is expressed in terms of the closure condition involving the epigraph of the conjugate of Fitzpatrick function associated with , and the operator As an easy application, a dual criterion for the maximality of the sum of two maximal monotone operators is also given. The work of this author was completed while at the School of Mathematics, University of New South Wales, Sydney, Australia.