
Journal of Convex Analysis 16 (2009), No. 3, 713725 Copyright Heldermann Verlag 2009 On Two Properties of Enlargements of Maximal Monotone Operators Radu Ioan Bot Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany radu.bot@mathematik.tuchemnitz.de Ernö Robert Csetnek Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany robert.csetnek@mathematik.tuchemnitz.de [Abstractpdf] We give an answer to an open problem regarding the full enlargeability of a maximal monotone operator $S:X\rightrightarrows X^*$ by $S^{se}$, the smallest enlargement belonging to a certain class of enlargements associated to $S$. Moreover, we prove the weak$^*$ closedness of the set $S_{h_S}(\varepsilon_1,x)+T_{h_T} (\varepsilon_2,x)$ under a weak generalized interior regularity condition. Keywords: Monotone operator, Fitzpatrick function, representative function, enlargement, subdifferential. MSC: 47H05, 46N10, 42A50 [ Fulltextpdf (157 KB)] for subscribers only. 