In short, a Hilbert Space is a mathematical construct such that within any plenum of n-dimensional spaces there exists an infinite number of said Hilbert Spaces (subsumed within an n+1 dimensional superset). Fancifully, science fiction writers point to the infinite plurality of 4D Hilbert Spaces that could exist within our "normal" 5D continuum, and suggest that each such Hilbert Space may really exist and that these Hilbert Spaces could be engendered by time-travel to the past. Thus, each 4D Hilbert Space in a 5D superset of "Universes" could possess a unique history, entirely different from all other universes contained within the 5D "Universe".
Deciphering Mozart's musical cryptography provides physical evidence that Hilbert Spaces may be entirely real, and not merely imaginary constructs.
Up to equivalence of norms, there's only one distinct n-dimensional Hilbert space for each n, namely R^n.