PreHilbertSpace

Is synonymous with InnerProductSpace.

When you encounter the term "pre-Hilbert space" in functional analysis literature like Yosida's Functional Analysis, you can substitute it with "inner-product space". The term "pre-Hilbert space" is often used to emphasize that we are dealing with an inner-product space that is not necessarily complete, i.e., it might not be a Hilbert space. But the main structure is still that of an inner-product space.