We revisit the computation of (2-modified) Fredholm determinants for operators with matrix-valued semi-separable integral kernels. The latter occur, for instance, in the form of Green’s functions associated with closed ordinary differential operators on arbitrary intervals on the real line. Our approach determines the (2-modified) Fredholm determinants in terms of solutions of closely associate...

Kato's decomposition [14, Theorem 4] is generalized to semi-B-Fredholm operators.

We consider the two-dimensional time-harmonic elastic wave scattering problem for an unbounded rough surface, due to an inhomogeneous source term whose support lies within a finite distance above the surface. The rough surface is supposed to be the graph of a bounded and uniformly Lipschitz continuous function, on which the elastic displacement vanishes. We propose an upward propagating radiati...

A Banach space operator T ∈ B(X ) is polaroid if points λ ∈ isoσσ(T ) are poles of the resolvent of T . Let σa(T ), σw(T ), σaw(T ), σSF+(T ) and σSF−(T ) denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower semi–Fredholm spectrum of T . For A, B and C ∈ B(X ), let MC denote the operator matrix (

The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most important classical definitions. We give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover, we establish...