  We find simple conditions for a non-negative Hankel quadratic form to be
closable. Under some mild a priori assumption on the associated moments these
sufficient conditions turn out to be also necessary. We also describe the
domain of the corresponding closed form. This allows us to define unbounded
non-negative Hankel operators under minimal assumptions on their matrix
elements. The results obtained supplement the classical Widom condition for a
Hankel operator to be bounded..
