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Measures of noncompactness and upper semi-Fredholm perturbation theorems. (English) Zbl 0782.47013

The author presents a general approach to the question of obtaining perturbation theorems for upper semi-Fredholm operators \(T\in \varphi_ +(x,y)\) with finite-dimensional null space and closed range. He constructs, for each perturbation function, characteristics \(\Delta\) and \(\Gamma\) similar to those given by Schechter. Several examples are presented with the perturbation function constructed. Also formulas for the essential spectral radius and the upper semi-Fredholm radius are given.
Reviewer: H.S.Nur (Fresno)

MSC:

47A55 Perturbation theory of linear operators
47A53 (Semi-) Fredholm operators; index theories
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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