Is every Pre-Hilbert space reflexive? Good day, It is known that every Hilbert space is reflexive. Does the same hold true for Pre-Hilbert spaces? I guess not since completeness is a pretty strong property that is now missing and the classical proof (as a corollary by Riesz) shouldn't work anymore. What do you think? So if they are not reflexive could you give me an example of an non-reflexive Pre-Hilbert space? Thanks a lot, Marvin

No, if a pre-Hilbert space is not complete it is not reflexive, dual spaces are always complete! On the other hand if a pre-Hilbert space is complete, it is a Hilbert space.