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Determinant Systems Method for Computing Reflexive Generalized Inverses of Products of Fredholm Operators

Gra ˙zyna Ciecierska

In the paper, for given Fredholm operators A ∈ L(Y, Z) and B ∈ L(X, Y ), an explicit construction for reflexive generalized inverses of A and B such that their product in reverse order is a reflexive generalized inverse of AB, is provided. In this approach, based on results of the theory of determinant systems, the correspondence between considered Fredholm operators and their determinant systems is applied.