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Multilinear mappings, tensor products, restrictions to finite dimensional spaces and differential calculus may all be used to define polynomials over infinite dimensional spaces. All of these are useful, none should be neglected and, indeed, the different possible approaches and interpretations add to the richness of the subject. We adopt an integrated approach to the development of polynomials using multilinear mappings and tensor products. The philosophy of tensor products is easily stated: to exchange polynomial functions on a given space with simpler (linear) functions on a (possibly) more complicated space.
KeywordsBanach Space Convex Space Normed Linear Space Bounded Subset Finite Dimensional Subspace
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