Isomorphic copies of ℓ1 for m-homogeneous non-analytic Bohnenblust–Hille polynomials

Abstract

We employ a classical result by Toeplitz (1913) and the seminal work by Bohnenblust and Hille on Dirichlet series (1931) to show that the set of continuous m-homogeneous non-analytic polynomials on c0 contains an isomorphic copy of ℓ1. Moreover, we can have this copy of ℓ1 in such a way that every non-zero element of it fails to be analytic at precisely the same point.