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Continuous dependence of solutions of operator equations. I


Author: Zvi Artstein
Journal: Trans. Amer. Math. Soc. 231 (1977), 143-166
MSC: Primary 47H15
DOI: https://doi.org/10.1090/S0002-9947-1977-0445351-1
MathSciNet review: 0445351
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Abstract: Continuous dependence of the solutions of the operator equation $ x = Tx + z$ in a topological vector space is the main subject of the paper. We find sufficient and necessary conditions for the continuous dependence on the data (T, z) or on a parameter. We do it for the space of all closed operators. Equivalent conditions for particular subfamilies are discussed. Among other families we deal with compact operators, compact perturbations of the identity, condensing operators and demicompact operators.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0445351-1
Keywords: Continuous dependence on parameters, closed operators, compact operators, condensing operators, fixed points, ODE, FDE
Article copyright: © Copyright 1977 American Mathematical Society

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