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Proceedings of the American Mathematical Society

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

 

 

Strongly dissipative operators and nonlinear equations in a Fréchet space


Author: R. H. Martin
Journal: Proc. Amer. Math. Soc. 32 (1972), 161-168
MSC: Primary 47H15
DOI: https://doi.org/10.1090/S0002-9939-1972-0295163-8
MathSciNet review: 0295163
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Abstract: Suppose that X is a Fréchet space, Y is a Banach subspace of X, and A is a function from Y into X. Sufficient conditions are determined to insure that the equation $ Ax = y\;(y \in Y)$ has a unique solution $ {x_y}$ which depends continuously on y. The techniques of this paper use the theory of dissipative operators in a Banach space, and the results are associated with the idea of admissibility of the space y. Also, the equation $ Ax = Cx + y$ is considered where C is completely continuous.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0295163-8
Keywords: Fréchet space, dissipative operator, nonlinear operator equation, admissibility
Article copyright: © Copyright 1972 American Mathematical Society