PT and CPT symmetries for non-Hermitian operators

In the present paper we enlarge the Max Planck law E = h(Ω 1 + Ω 2 ) for non-Hermitian operators and have examined the behavior of PT and CPT symmetries. For a quantum theory based on a non-Hermitian Hamiltonian, the spectrum in the general case is complex, and the time-evolution is non-unitary. We study also the case of non-commutative and non-Hermitian deformed harmonic oscillator and the behaviour of CPT symmetry. For further research, there appears the main problem of the connection between noncommutative geometry for non-Hermitian operators just as the conservation or not of PT and CPT symmetries.