Uber die fredholm-alternative bei linearen approximationsregularen operatoren

Abstract

In this paper some recent results of Petryshyn on linear A-proper mappings are generalized to linear operators A : E? F which form together with a sequence (A_i) of operators A_iE_i? F_i ? A_o, a so called a-regular pair. The operators A_i have to be understood as approximations to A satisfying the condition of a-regularity, which is a characteristic property in studying the convergence of approximation methods. The theorems proved in this paper are concerned with properties shared by an operator A, if there exists a sequence (A _i), such that the pair A,(A_i) is a regular. One of the main results is that, under this condition, A satisfies a generalized Fredholm-Alternative