Abstract
In this paper we present a dual criterion for the maximal monotonicity of the composition operator \(T:=A^{\ast }SA\), where \(S:Y\rightrightarrows Y^{\,{\prime }}\) is a maximal monotone (set-valued) operator and \(A: X\rightarrow Y\) is a continuous linear map with the adjoint \(A^{\ast }\), \(X\) and \(Y\) 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 \(S\), and the operator \(A.\) As an easy application, a dual criterion for the maximality of the sum of two maximal monotone operators is also given.
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The work of this author was completed while at the School of Mathematics, University of New South Wales, Sydney, Australia.
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Jeyakumar, V., Wu, Z.Y. A Dual Criterion for Maximal Monotonicity of Composition Operators. Set-Valued Anal 15, 265–273 (2007). https://doi.org/10.1007/s11228-006-0025-5
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DOI: https://doi.org/10.1007/s11228-006-0025-5
Key words
- composition operators
- maximal monotonicity
- maximality of sum of two maximal monotone operators
- dual conditions