Structure Theory for Maximally Monotone Operators with Points of Continuity

  • Jonathan M. Borwein
  • Liangjin YaoEmail author
Invited Paper


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.


Local boundedness Maximally monotone operator Monotone operator Norm-weak graph closedness Property (Q) 



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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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.CARMAUniversity of NewcastleNewcastleAustralia

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