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In this paper we study truncated moment problems for $J$-self-adjoint,$J$-skew-self-adjoint and $J$-unitary operators. Conditions of the solvabilityare given. Some canonical solutions of the moment problems are constructed. Asa by-product, some extension results for $J$-skew-symmetric and $J$-isometricoperators are obtained.

Truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators