  The purpose of this paper is to prove that the spectrum of the
non-self-adjoint one-particle Hamiltonian proposed by J. Feinberg and A. Zee
(Phys. Rev. E 59 (1999), 6433--6443) has interior points. We do this by first
recalling that the spectrum of this random operator is the union of the set of
$\ell^\infty$ eigenvalues of all infinite matrices with the same structure. We
then construct an infinite matrix of this structure for which every point of
the open unit disk is an $\ell^\infty$ eigenvalue, this following from the fact
that the components of the eigenvector are polynomials in the spectral
parameter whose non-zero coefficients are $\pm 1$'s, forming the pattern of an
infinite discrete Sierpinski triangle.
