Abstract

The relationship between the generalized invertibility of a general Wiener-Hopf operator P 2 A∣ImP1 acting from a Banach space X into a Banach space Y (P 1, P 2 are projections on X,Y, respectively, and A : X → Y is bounded invertible) and the existence of a decomposition of the space as a direct sum of certain subspaces of Y related to Im (AP 1) and Ker P 2 is examined. The explicit calculation of the projection associated with this decomposition is studied. An example corresponding to a singular integral equation on a finite interval is given.

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