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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Ranges of perturbed maximal monotone and $ m$-accretive operators in Banach spaces

Authors: Zhengyuan Guan and Athanassios G. Kartsatos
Journal: Trans. Amer. Math. Soc. 347 (1995), 2403-2435
MSC: Primary 47H05; Secondary 47H06, 47H11, 47H15
MathSciNet review: 1297527
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Abstract: A more comprehensive and unified theory is developed for the solvability of the inclusions $ S \subset \overline {R(A + B)} $, int $ S \subset R(A + B)$, where $ A:X \supset D(A) \to {2^Y}$, $ B:X \supset D(B) \to Y$ and $ S \subset X$. Here, $ X$ is a real Banach space and $ Y = X$ or $ Y = {X^*}$. Mainly, $ A$ is either maximal monotone or maccretive, and $ B$ is either pseudo-monotone or compact. Cases are also considered where $ A$ has compact resolvents and $ B$ is continuous and bounded. These results are then used to obtain more concrete sets in the ranges of sums of such operators $ A$ and $ B$. Various results of Browder, Calvert and Gupta, Gupta, Gupta and Hess, and Kartsatos are improved and/or extended. The methods involve the application of a basic result of Browder, concerning pseudo-monotone perturbation of maximal monotone operators, and the Leray-Schauder degree theory.

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Keywords: Maximal monotone operator, pseudo-monotone operator, $ m$-accretive operator, compact perturbation, compact resolvent, range of sums
Article copyright: © Copyright 1995 American Mathematical Society