Abstract
Within a nonzero, real Banach space we show that a monotone operator with a bounded domain that is representable by a representative function with a bigger conjugate must be maximal. This study allows us to resolve some long outstanding questions in the area. It follows that all maximal monotone operators are of type FPV and their domains have a convex closure.
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This paper is dedicated to the memory of Charles Pearce.
The first author’s research was funded by ARC grant # DP120100567.
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Eberhard, A., Wenczel, R. All Maximal Monotone Operators in a Banach Space are of Type FPV. Set-Valued Var. Anal 22, 597–615 (2014). https://doi.org/10.1007/s11228-014-0275-6
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DOI: https://doi.org/10.1007/s11228-014-0275-6