Extendibility of polynomials and analytic functions on ℓp

Abstract

We prove that extendible 2-homogeneous polynomials on spaces with co-type 2 are integral. This allows us to find examples of approximable non-extendible polynomials on ℓp (1 ≤ p < ∞) of any degree. We also exhibit non-nuclear extendible polynomials for 4 < p < ∞. We study the extendibility of analytic functions on Banach spaces and show the existence of functions of infinite radius of convergence whose coefficients are finite type polynomials but which fail to be extendible.