Truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint   and $J$-unitary operators
  In this paper we study truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators. Conditions of the solvability are given. Some canonical solutions of the moment problems are constructed. As a by-product, some extension results for $J$-skew-symmetric and $J$-isometric operators are obtained. 
Sergey M. Zagorodnyuk
math.FA