We utilize a recently developed formalism for the construction of effe
ctive operators to discuss the construction of and relation between he
rmitian and non-hermitian effective operators in the energy independen
t Suzuki and Lee approach. Our original formalism is applicable to ope
rators that need not be hermitian or quasi-hermitian in the full space
(e.g. operators obtained by boson mapping). Here we show that if the
full space Hamiltonian of the system is indeed hermitian, results of t
he formalism can be expressed and interpreted in the context of quasi-
hermitian operators to facilitate a transparent construction of effect
ive operators which are energy independent and manifestly hermitian.