We consider linear operator equations of the so called second kind which are of the form
$$ {\text{x}} - {\text{Kx}} = \left( {{\text{I}} - {\text{K}}} \right){\text{x}} = {\text{y}} $$
where K is a continuous linear operator mapping a Banach space X into itself and I:X→X denotes the identical mapping. We assume that the inverse (I-K)-1 of (I-K) exists on X and is continuous so that for each choice of y∈X the equation (1.1) has a unique solution x∈X.


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© Springer Basel AG 1979

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  • W. Krabs

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