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Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by meansof the algebraic method which was originally proposed for the pseudo-HermitianHamiltonian systems rather than for the PT-symmetric ones. Compared with theway converting a non-Hermitian Hamiltonian to its Hermitian counterpart, thismethod has the merit that keeps the Hilbert space of the non-HermitianPT-symmetric Hamiltonian unchanged. In order to give the positive definiteinner product for the PT-symmetric systems, a new operator V, instead of C, canbe introduced. The operator V has the similar function to the operator Cadopted normally in the PT-symmetric quantum mechanics, however, it can beconstructed, as an advantage, directly in terms of Hamiltonians. The spectra ofthe two non-Hermitian PT-symmetric systems are obtained, which coincide withthat given in literature, and in particular, the Hilbert spaces associated withpositive definite inner products are worked out.

Investigation of PT-symmetric Hamiltonian systems from an alternative point of view