Approximations in the l∞ norm and the generalized inverse

AbstractWe introduce the concept of a strict l∞-metric projector, based in the definition of strict approximation, to prove that for each matrix A of order m×n with coefficients in the field R of real numbers there exists a set of operators G: Rm → Rn homogeneous and continuous, but not necessarily linear (strict generalized inverse) such that AGA = A and ‖AGy−y‖ is minimized for all y, when the norm is the l∞ norm. We investigate the properties of these operators and prove that there are two distinguished operators A-1∞, β and A-1∞ which are extensions of the generalized inverse introduced by Newman and Odell in the case of a strictly convex norm