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An application of Plemelj-Smithies formulas to computing generalized inverses of Fredholm operators

Ciecierska G.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 1

13--26

We consider continuous operators S +T in Banach spaces, where S is Fredholm and T is quasinuclear. By referring to the basic result of the Fredholm theory, i.e. to the expression of the resolvent ( I + λT ) −1 of the operator T as a quotient of entire functions of λ , we derive analogous formulas for generalized inverses of operators S +T. We apply the Plemelj-Smithies formulas describing terms of determinant systems for the quasinuclear perturbations of Fredholm operators.