
Journal of Convex Analysis 07 (2000), No. 1, 115128 Copyright Heldermann Verlag 2000 Regular Maximal Monotone Operators and the Sum Theorem Andrei Verona Dept. of Mathematics, California State University, Los Angeles, CA 90032, U.S.A. Maria Elena Verona Dept. of Mathematics, University of Southern California, Los Angeles, CA 900891113, U.S.A. In this note, which is a continuation of a previous paper of the authors [SetValued Analysis 6 (1998) 302312], we study two classes of maximal monotone operators on general Banach spaces which we call C_{0} (resp. C_{1})regular. All maximal monotone operators on a reflexive Banach space, all subdifferential operators, and all maximal monotone operators with domain the whole space are C_{1}regular and all linear maximal monotone operators are C_{0}regular. We prove that the sum of a C_{0} (or C_{1})regular maximal monotone operator with a maximal monotone operator which is locally inf bounded and whose domain is closed and convex is again maximal monotone provided that they satisfy a certain "domdom" condition. From this result one can obtain most of the known sum theorem type results in general Banach spaces. We also prove a local boundedness type result for pairs of monotone operators. [ Fulltextpdf (214 KB)] 