Abstract

We study properties of ultramaximally monotone operators. We characterize the interior and the closure of the range of an ultramaximally monotone operator. We establish the Brezis-Haraux condition in the setting of a general Banach space. Moreover, we show that every ultramaximally monotone operator is of type (NA), which generalizes Bauschke and Simons' result.

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Keywords

  • Brézis-Haraux condition
  • Fenchel conjugate
  • Fitzpatrick function
  • linear relation
  • maximally monotone operator
  • monotone operator
  • operator of type (D)
  • operator of type (NI)
  • operator of type (NA)
  • rectangular
  • set-valued operator
  • subdifferential operator
  • ultramaximally monotone operator

Mathematics Subject Classification

47H05, 47N10, 47B65; 90C25

Suggested citation

L. Yao. “Finer Properties of Ultramaximally Monotone Operators on Banach Spaces.” Journal of Convex Analysis 23 (2016), No. 4, 1205–1218. https://doi.org/10.68381/jca23045

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Published by Heldermann Verlag, 2016. Rights now held by Banach Press.