The eigenvalue equation in the Dyson boson mapping is non-Hermitian. A method for a Hermitian treatment of this non-Hermitian eigenvalue equation has been proposed by one of the present authors.1) If we intend to apply this method to realistic cases, we cannot help retaining only a small number of degrees of freedom which are important for describing the collective motions of interest. In such cases, this method would be an approximation. In the present paper, we test the validity of this approximation in numerical calculations for some realistic nuclei. The results show that this method of Hermitian treatment is a very good approximation within truncated boson subspaces.
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