We define a notion of topological degree for a class of maps (called orientable), defined between real Banach spaces, which are Fredholm of index zero. We introduce first a notion of orientation for any linear Fredholm operator of index zero between two real vector spaces. This notion (which does not require any topological structure) allows to define a concept of orientability for nonlinear Fr...

It is shown that the inverse scattering problem for the three-dimensional SchrSdinger equation with a potential having no spherical symmetry can be solved using a Fredholm integral equation. The integral operator studied here is shown to be compact and self-adjoint with its spectrum in [-1, 1]. The relationship between solutions of this Fredholm equation and of a related RiemannHilbert problem ...

Co-author: Lúıs Castro We will present a study of the Fredholm property for matrix Wiener-Hopf plus/minus Hankel operators with semi-almost periodic Fourier symbols. The Fredholm property will be described based on certain factorizations of the representatives at infinity of the original symbols, and on the geometrical mean values of the corresponding factors. The Fredholm indices of those oper...

In [24], Koliha proved that T ? L(X) (X is a complex Banach space) generalized Drazin invertible operator iff there exists an S commuting with such STS = and ?(T2S?T) {0} 0 < acc ?(T). Later, in [14, 34] the authors extended class of operators they also pseudo-Fredholm introduced by Mbekhta [27] other classes semi-Fredholm operators. As continuation these works, we introduce study 1zinvertib...

For A ? L(X), B L(Y) and C L(Y,X) we denote by MC the operator matrix defined on X Y = (A 0 B). In this paper, prove that ?qF(A) ?qF(B) [ C?L(Y,X) ?qF(MC) ?p(B) ?p(A?), where ?qF(.) (resp. ?p(.)) denotes quasi-Fredholm spectrum point spectrum). Furthermore, consider some sufficient conditions for to be have ?qF(MC).