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

Abstract

We consider continuous operators T S + 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 ( ) 1 − + T I λ of the operator T as a quotient of entire functions of λ , we derive analogous formulas for generalized inverses of operators T S + . We apply the Plemelj-Smithies formulas describing terms of determinant systems for the quasinuclear perturbations of Fredholm operators.