Continuous dependence of solutions of operator equations. I

Artstein, Zvi

doi:10.1090/S0002-9947-1977-0445351-1

Continuous dependence of solutions of operator equations. I
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Trans. Amer. Math. Soc. 231 (1977), 143-166 Request permission

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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Sur les espaces completes

15

Topology

36

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Nonexpansive and monotone mappings in Banach spaces

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