The operator theory on the indefinite inner product spaces is not a simple logical extension of the operator theory in the Hilbert space but has a profound foundation. Its application involves physics, mathematics, and mechanics. The space of “time-space” in relativity is an indefinite inner product space. The indefinite inner product space first appeared in the article of P. A. M. Dirac (see [88]) about quantum field theory and was then widely used in the field of quantum field theory. The Li-Wick theory proposed by Zhengdao Li and G. C. Wick is a theory that uses the indefinite inner product to eliminate the divergence difficulty in quantum field theory. Later, L. S. Pontryagin (see [89]) explored the operator theory in indefinite inner product spaces from a mathematical perspective due to the need for the study of mechanical problems.