  In this paper we consider a twofold Ellis-Gohberg type inverse problem in an
abstract *-algebraic setting. Under natural assumptions, necessary and
sufficient conditions for the existence of a solution are obtained, and it is
shown that in case a solution exists, it is unique. The main result relies
strongly on an inversion formula for a $2\times 2$ block operator matrix whose
off diagonal entries are Hankel operators while the diagonal entries are
identity operators. Various special cases are presented, including the cases of
matrix-valued $L^1$-functions on the real line and matrix-valued Wiener
functions on the unit circle of the complex plane. For the latter case, it is
shown how the results obtained in an earlier publication by the authors can be
recovered.
