Let 7(S) denote the reduced minimum modulus of a linear operator S acting in a complex Banach space X, and let / denote the identity on X. In this paper it is shown that for a (not necessarily bounded) Fredholm operator T acting in X, the limit lim y^fy/rt exists and is equal to the supremum of all positive numbers S such that the dimension of the null space and the codimension of the range of ...

Operators of Wiener-Hopf plus Hankel type have been receiving an increasing attention in the last years (see [1, 2, 4, 6, 10, 12–16]). Some of the interest in their study arises directly from concrete applications where these kind of operators appear. This is the case in problems of wave diffraction by some particular rectangular geometries which originate specific boundary-transmission value p...

The two-point time and temperature dependent correlation functions for the XX0 one-dimensional model in constant magnetic field are represented (in the thermodynamical limit) as Fredholm determinants of linear integral operators.

We describe the generic behavior of Fredholm indices in the space of Toeplitz operators. We relate this behavior to certain conjectures and open problems that arise in the context of the Quantum Hall Effect.

Fredholm determinant asymptotics of convolution operators on large finite intervals with rational symbols having real zeros are studied. The explicit asymptotic formulae obtained can be considered as a direct extension of the Ahiezer-Kac formula to symbols with real zeros.

A general integral formula for the spectral flow of a path of unbounded selfadjoint Fredholm operators subject to certain summability conditions is derived from the interpretation of the spectral flow as a winding number.

The invertible, compact and Fredholm multiplication operators on generalized Lorentz-Zygmund (GLZ) spaces Lp,q;α, 1 < p ≤ ∞, 1 ≤ q ≤ ∞, α in the Euclidean space R, are characterized in this paper.