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We sharpen and extend inequalities concerning generalized inverses previously obtained for the von Neumann-Schatten, and supremum, norms. We sharpen those inequalities to obtain corresponding inequalities for singular values Si(·) for i=1,2…; and we extend those inequalities, for finite rank operators, to inequalities for an arbitrary unitarily invariant norm.

Some singular values and unitarily invariant norm inequalities concerning generalized inverses