  An elegant but elementary result of Wolff from 1921, when interpreted in
terms of Banach algebras, shows that it is possible to find a sequence of
distinct characters $\phi_n$ on the disc algebra and an $\ell_1$ sequence of
complex numbers $\lambda_n$, not all zero, such that $\sum_{n=1}^\infty
\lambda_n \phi_n =0.$ We observe that, even for general commutative, unital
Banach algebras, this is not possible if the closure of the countable set of
characters has no perfect subsets.
