  The eigenstates of a diagonalizable PT-symmetric Hamiltonian satisfy
unconventional completeness and orthonormality relations. These relations
reflect the properties of a pair of bi-orthonormal bases associated with
non-hermitean diagonalizable operators. In a similar vein, such a dual pair of
bases is shown to possess, in the presence of PT symmetry, a Gram matrix of a
particular structure: its inverse is obtained by simply swapping the signs of
some its matrix elements.
