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The "generalized Weyl" operators between two Hilbert spaces are taken to be those with closed range for which the null space and that of the adjoint are of equal Hilbert space dimension. We show that products of two of these which happen to have closed range, and finite rank perturbation of these, are also generalized Weyl.doi:10.1090/s0002-9939-01-06081-6 fatcat:gykbbjpepzcktpxz7krj2wp254