A frequency domain solution to the sub-optimal Hankel norm approximation problem

An elementary proof is presented for sufficient conditions for the existence of a solution to the sub-optimal Hankel norm approximation problem for the class of matrix-valued continuous functions defined on the imaginary axis with limit $\;0\;$ at $\;\pm \infty\;$ in terms of a solution to a certain $\;J-$spectral factorization problem. All solutions are parameterized in terms of the $\;J-$spectral factor