  Most recently it has been observed e.g. by Bender and Klevansky
(arXiv:0905.4673 [hep-th]) that the C-operator related to a PT-symmetric
non-Hermitian Hamilton operator is not unique. Moreover it has been remarked by
Shi and Sun (arXiv:0905.1771 [hep-th]) very recently that there seems to exist
a well defined inner product in the context of the Hamilton operator of the
PT-symmetric non-Hermitian Lee model yielding a different C-operator as
compared to the one previously derived by Bender et al.. The puzzling
observations of both manuscripts are reconciled and explained in the present
manuscript as follows: the actual form of the metric operator (and the induced
C-operator) related to some non-Hermitian Hamilton operator constructed along
the lines of Shi and Su depends on the chosen normalization of the left and
right eigenvectors of the Hamilton operator under consideration and is
therefore ambiguous. For a specific PT-symmetric 2x2-matrix Hamilton operator
it is shown that - by a suitable choice of the norm of its eigenvectors - the
metric operator yielding a positive semi-definite inner product can be made
even independent of the parameters of the considered Hamilton operator. This
surprising feature makes in turn the obtained metric operator rather unique and
attractive. For later convenience the metric operator for the Bosonic and
Fermionic (anti)causal harmonic oscillator is derived.
