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It is shown that for each closed subset Ω \Omega of the semi-Fredholm domain of a bounded linear operator T T acting in a complex Hilbert space H H there exists a subspace of a finite codimension in H H such that the compression of T − λ T - \lambda to this subspace is a left- or right-invertible operator for all λ \lambda in Ω \Omega . From this result we obtain a characterization of the Weyl spectrum of T T .

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