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Proceedings of the American Mathematical Society

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

 

 

An elementary proof of surjectivity for a class of accretive operators


Author: William O. Ray
Journal: Proc. Amer. Math. Soc. 75 (1979), 255-258
MSC: Primary 47H06; Secondary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1979-0532146-0
MathSciNet review: 532146
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Abstract: An operator A defined on a real Banach space X is said to be locally accretive if, for each $ \lambda > 0,x \in X$ and each y near x, $ x,\left\Vert {x - y} \right\Vert \leqslant \left\Vert {x - y + \lambda (Ax - Ay)} \right\Vert$. It is shown that if $ A:X \to X$ is locally accretive and locally Lipschitzian then $ (I + A)(X) = X$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0532146-0
Keywords: Locally accretive, m-accretive
Article copyright: © Copyright 1979 American Mathematical Society