  General properties of eigenvectors and eigenvalues for an effective
Hamiltonian governing time evolution in a two state subspace of the state space
of the total system under consideration are discussed. The Lee, Oehme and Yang
(LOY) theory of time evolution in such a subspace and CP-- and CPT--symmetry
properties of the LOY effective Hamiltonian are considered. The CPT
transformation properties of the exact effective Hamiltonian for two state
subspace are discussed also. Using the Khalfin Theorem we show that contrary to
the properties of the LOY theory, the diagonal matrix elements of the exact
effective Hamiltonian governing the time evolution in the subspace of states of
an unstable particle and its antiparticle need not be equal at for $t > t_{0}$
($t_{0}$ is the instant of creation of the pair) when the total system under
consideration is CPT invariant but CP noninvariant. Using the more accurate
approximation than the LOY one we show that the interpretation of the tests
measuring the difference between the $K_{0}$ mass and the ${\bar K}_{0}$ mass
as the CPT--symmetry test is wrong.
