  Let $\Omega$ be a proper open cone in a real Banach space $V$. We show that
the tube domain $V \oplus i\Omega$ over $\Omega$ is biholomorphic to a bounded
symmetric domain if and only if $\Omega$ is a normal linearly homogeneous
Finsler symmetric cone, which is equivalent to the condition that $V$ is a
unital JB-algebra in an equivalent norm and $\Omega$ is the interior of $\{v^2:
v\in V\}$.
