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Structure Theory for Maximally Monotone Operators with Points of Continuity

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Abstract

In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of norm-to-weak∗ closedness and of property (Q) for these operators (as recently proven by Voisei). Various applications and limiting examples are given.

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Acknowledgements

Both authors were partially supported by various Australian Research Council grants. They thank Dr. Brailey Sims for his helpful comments, and also thank a referee for his/her careful reading and pertinent comments. The authors especially thank Dr. Robert Csetnek for his many constructive and helpful comments.

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Authors and Affiliations

  1. CARMA, University of Newcastle, Newcastle, New South Wales, 2308, Australia

    Jonathan M. Borwein & Liangjin Yao

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  1. Jonathan M. Borwein
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  2. Liangjin Yao
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Correspondence to Liangjin Yao.

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J.M. Borwein is Laureate Professor at the University of Newcastle and Distinguished Professor at King Abdul-Aziz University, Jeddah.

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Borwein, J.M., Yao, L. Structure Theory for Maximally Monotone Operators with Points of Continuity. J Optim Theory Appl 157, 1–24 (2013). https://doi.org/10.1007/s10957-012-0162-y

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  • DOI: https://doi.org/10.1007/s10957-012-0162-y

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