  In this note, we find sufficient conditions for an operator with kernel of
the form $A(x)B(y)-A(x)B(y)/(x-y)$ (which we call a Tracy-Widom type operator)
to be the square of a Hankel operator. We consider two contexts: infinite
matrices on $\ell^2$, and integral operators on the Hardy space
$H^2(\mathbb{T})$. The results can be applied to the discrete Bessel kernel,
which is significant in random matrix theory.
