The relations of similarity, quasi-similarity, almost similarity, asymptotic similarity and compalence are discussed in this paper. Various spectral results on these notions are presented. In addition, we establish the ...

We study the spectrum of Schrodinger operator P (h) for a polyatomic molecul in the Born-Oppenheimer approximation where the mass ratio h2 of electronic to nuclear mass tends to zero. We prove that this study can be reduced ...

P=− d 2 dx2+ V, where V is a periodic real function. Essentially we show that the spectra of these operators can be determined by a smooth function α, the phase of the eigenvalues of a matrix M (E, x, V) expressing the ...

We present a general reduction Feshbach method that can be applied in particular to the spectral study of operators including the hamiltonian of the Born-Oppenheimer approximation and also to Fredholm operators. This ...

Let C(H) be the set of all linear closed operators densely defined on a Hilbert space H. This paper is devoted to the study of the equivalent statements for which an operator A belongs to C(H) has a closed range.

In this article, we show the existence and uniqueness of positive solutions for perturbed Neumann boundary-value problems of second-order differential equations. We use a fixed point theorem for general -concave operators.

JP Labrousse [8] studied and characterized in the case of Hilbert spaces, a relation between the Kato essential spectrum (essential quasi-Fredholm spectrum) and another essential spectrum defined by σec (T)= 1λ∈ C; R (λI-T) ...

In this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a ...

The main subject of this paper is the study of a general linear boundary-value problem with Drazin or right Drazin (respectively, left Drazin) invertible operators corresponding to initial boundary operators. The obtained ...

When A∈ B (H) and B∈ B (K) are given, we denote by MC the operator on the Hilbert space H⊕ K of the form MC=(AC 0 B). In this paper we investigate the quasi-nilpotent part and the analytical core for the upper triangular ...