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.