Perturbation theory for generalized Fredholm operators

Fredholm Operators and the Generalized Index

One of the most fundamental problems in mathematics is to solve linear equations of the form Tf = g, where T is a linear transformation, g is known, and f is some unknown quantity. The simplest example of this comes from elementary linear algebra, which deals with solutions to matrix-vector equations of the form Ax = b. More generally, if V,W are vector spaces (or, in particular, Hilbert or Ban...

Perturbation Results on Semi-Fredholm Operators and Applications

We give some results concerning stability in the Fredholm operators and Browder operators set, via the concept of measure of noncompactness. Moreover, we prove some localization results on the essential spectra of bounded operators on Banach space. As application, we describe the essential spectra of weighted shift operators. Finally, we describe the spectra of polynomially compact operators, a...

Perturbation and Coperturbation Functions Characterising Semi-fredholm-type Operators

Certain norm-related functions have been considered in order to obtain characterisations and perturbation results for various classes of semi-Fredholm-type operators. In the §2, by means of what we have called a perturbation function, we present a general approach to the question of obtaining characterisations and perturbation theorems for F + and strictly singular operators. To this end, for e...

Perturbation of a Fredholm Complex by Inessential Operators

The work of Ambrozie and Vasilescu on perturbations of Fredholm complexes is generalized by discussing the stability theory of Banach space complexes under inessential perturbations. 2000 Mathematics Subject Classification: Primary: 47A53; Secondary: 47A13.

Research Article Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators