Simplicity principle for nonreal periodic and antiperiodic eigenvalues

Let $L(V)$ be the operator in the paper, and let periodic and antiperiodic eigenvalues mean Bloch eigenvalues with the corresponding periodic or antiperiodic boundary condition. Simplicity principle. The nonreal periodic and antiperiodic eigenvalues are simple eigenvalues. The principle is introduced as an assumption for the discussion of the spectral expansion, and no resolution is supplied in the given text.