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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Sets in the ranges of sums for perturbations of nonlinear $ m$-accretive operators in Banach spaces


Author: Athanassios G. Kartsatos
Journal: Proc. Amer. Math. Soc. 123 (1995), 145-156
MSC: Primary 47H15; Secondary 47H06, 47H10
DOI: https://doi.org/10.1090/S0002-9939-1995-1213863-5
MathSciNet review: 1213863
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Abstract: Several results are given involving nonlinear range inclusions of the types $ B + D \subset \overline {R(T + C)} $ and $ \operatorname{int} (B + D) \subset R(T + C)$, where B, D are subsets of a real Banach space X, the operator $ T:X \supset D(T) \to {2^X}$ is at least m-accretive, and the perturbation $ C:X \supset D(C) \to X$ is at least compact, or demicontinuous, or m-accretive. Leray-Schauder degree theory is used in most of the results, and extended versions of recent results of Calvert and Gupta, Morales, Reich, and the author are shown to be possible by using mainly homotopies of compact transformations.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1213863-5
Keywords: Accretive operator, m-accretive operator, compact perturbation, compact resolvent, range of sums, Leray-Schauder degree theory
Article copyright: © Copyright 1995 American Mathematical Society