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Let E be a complex Banach space and F be a complex Banach algebra. We will be interested in the subspace IPf ( E,F ) of P (E,F ) generated by the collection of functions φ(n ∈ , φ ∈ L(E,F )) where φ(x) = (φ(x)) for each x ∈ E.

A class of polynomials from Banach spaces into Banach algebras