Test of validity of the Hermitian treatment of the Dyson boson mapping

The eigenvalue equation in the Dyson boson mapping is non-Hermitian. A meth od 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 thi s method to realistic cases, we cannot help retaining only a small number o f degrees of freedom which are important for describing the collective moti ons of interest. In such cases, this method would be an approximation. Tn t he present paper, we test the validity of this approximation in numerical c alculations for some realistic nuclei. The results show that this method of Hermitian treatment is a very good approximation within truncated boson su bspaces.