  Let LT be a Lubin-Tate formal group attached to a finite extension of Qp. By
a theorem of Lubin-Sarkis, an invertible characteristic p power series that
commutes with the elements of Aut(LT) is itself in Aut(LT). We extend this
result to perfectoid power series, by lifting such a power series to
characteristic zero and using the theory of locally analytic vectors in certain
rings of p-adic periods. This allows us to recover the field of norms of the
Lubin-Tate extension from its completed perfection.
