Abstract
Given a bounded linear operatorA in an infinite dimensional Banach space and a compact subset Λ of a connected component of its semi-Fredholm domain, we construct a finite rank operatorF such that λ−A+F is bounded below (or surjective) for each λ ∈ Λ,F 2=0 and rankF=maxλ∈Λ min{dimN(λ−A), codimR(λ−A)}, if ind(λ−A)≤0 (or ind(λ−A)≥0, respectively) for each λ∈Λ.
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