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We present an optimization framework based on Lagrange duality and the scattering T-operator of electromagnetism to construct limits on the possible features that may be imparted to a collection of output fields from a collection of given input fields, i.e., constraints on achievable optical transformations and the characteristics of structured materials as communication channels. Implications of these bounds on the performance of representative optical devices having multiwavelength or multiport functionalities are examined in the context of electromagnetic shielding, focusing, near-field resolution, and linear math kernels.