Abstract
ABSTRACTLet be a Hilbert space, the algebra of bounded linear operators on and a positive operator. Given a closed subspace of , we characterize the shorted operator of W to as the maximum and as the infimum of certain sets, for the minus order . Also, given with closed range, we study the following operator approximation problem considering the minus order:We show that, under certain conditions, the shorted operator of is the minimum of this problem and we characterize the set of solutions.
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