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
liangjin.yao@umanitoba.ca
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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