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Journal of Convex Analysis 23 (2016), No. 4, 1205--1218
Copyright Heldermann Verlag 2016

Finer Properties of Ultramaximally Monotone Operators on Banach Spaces

Liangjin Yao
Dept. of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

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.

Keywords: Brezis-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 operat

MSC: 47H05, 47N10, 47B65; 90C25

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