Pseudo-Hermitian Hamiltonians and Generalized Involutory Symmetries*

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We propose definitions of generalized parity (P), time-reversal (T) and charge-conjugation (C) operators such, that any diagonalizable pseudo-Hermitian Hamiltonian is invariant under the involutory symmetries C, TP, and CPT. We inquire about the peculiarities of such symmetries showing that these constitute the P-unitary and P-antiunitary symmetry generators. Moreover, we give a necessary and sufficient condition for diagonalizable pseudo-Hermitian Hamiltonians to admit P-pseudounitary and P-pseudoantiunitary symmetries.

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