where η − $^{1}$Ψ$_{n}$ ( x ; m$_{+}$ ) = Φ$_{n}$ ( x ; m$_{+}$ ) ∈ L $^{2}$( R ) are the eigenfunctions for H$_{m}$$_{+}$ in the Hilbert space. Both the non-Hermitian complex P T -symmetric Hamiltonian H$_{PT}$$_{,m}$$_{+}$ and its Hermitian partner Hamiltonian H$_{m}$$_{+}$ are isospectral, therefore. Under such settings, we may observe that our examples in the previous section fit into such isospecrtrality argument, no doubt. However, an immediate example on ”temporary-fragile-isospectrality” may be sought in the complex P T -symmetric potential V ( x ) = − A sech $^{2}$( x − ic ). Which upon the de-Sitter anti-de-Sitter transformation would be mapped into V ( x ) = − A/ cos $^{2}$x that manifests an unbounded spectrum because of the nega- tive sign. Nonetheless, an immediate remedy may be sought in the parametriza- tion of the coupling parameter, i.e., A −→ − B ∈ R (in analogy with the mass parametrization in (9)). This would, in turn, take V ( x ) = − A/ cos $^{2}$x (which does not support bound states) into V ( x ) = B/ cos $^{2}$x ∈ R (which supports bound states). In due course, we find that the complex P T -symmetric Hamiltonians find their Hermitian partners in the regular Hilbert space through either a simple transformation toy (13) or a similarity transformation toy (23) accompanied by a mass parametrization recipe (9) and/or an analogous coupling constant recipe is an unavoidable conclusion. Nevertheless, having had established this fact, we may now try to explore the orthonormalization conditions. Since Φ$_{n}$ ( x ) ∈ L $^{2}$( R ) are the eigenfunctions for H in Hilbert space, they satisfy the regular quantum mechanical orthonor- malization condition Consequently, the established connection Φ$_{n}$ ( x ) = η − $^{1}$Ψ$_{n}$ ( x ) ∈ L $^{2}$( R ) would imply 11 〈 Φ$_{k}$ ( x ) | Φ$_{n}$ ( x ) 〉 = δ$_{kn}$. (29) 〈 η − $^{1}$Ψ$_{k}$ ( x ) ∣ η − $^{1}$Ψ$_{n}$ ( x ) 〉 = δ$_{kn}$. (30)