  In a paper from 2016 D. R. Yafaev initiated a study of closable Hankel forms
associated with the moments $(m_n)$ of a positive measure with infinite support
on the real line. If $m_n=o(1)$ Yafaev characterized the closure of the form
based on earlier work on quasi-Carleman operators. We give a new proof of the
description of the closure based entirely on moment considerations.
  The main purpose of the present paper is a description of the self-adjoint
Hankel operators associated with closed Hankel forms in the Hilbert space of
square summable sequences.
  We do this not only in the case $m_n=o(1)$ studied by Yafaev but also in two
other cases, where the Hankel form is closable, namely if the moment sequence
is indeterminate or if the moment sequence is determinate with finite index of
determinacy.
