I was surprised to see a reply to a comment on his answer to a Quora question by a research mathematician claiming that Hilbert spaces were actually due to J. W. Gibbs rather than to D. Hilbert. The Wikipedia entry for Hilbert spaces does not credit Gibbs at all, and the entry for Gibbs does not say enough to lead me to such a conclusion either. It is the case that in the entry for Hilbert spaces, applications to the phenomenon known as Gibbs phenomenon are briefly mentioned, but it’s not clear yet to me that anything in the Wikipedia entry for Gibbs phenomenon suggests that that topic was somehow the motivation for defining Hilbert spaces.
Consequently, in searching online for information about this but historical trivia led me to this site through the question at the following link:
The answers and comments there don’t seem to suggest either that J. W. Gibbs invented Hilbert spaces, so my question remains.