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Let X, Y, and Z be Banach spaces. Let T E K (X, Y) where K (X, Y) denotes the set of all compact operators from X to Y and S E B (Y, Z) where S is injective. Prove that for every 8 > 0 there is a constant C 2 0 such that ||T93||Y S ||~'B||X + CIISTalllz for all m E X