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Wikipedia details Von Neumann expanded Koopman’s 1931 Hilbert-Space work
Hilbert-space techniques are used for both quantum theory and classical physics, with the Koopman–von Neumann formulation and the method of “classical” wave functions being important examples. In 1931, Bernard Koopman published a paper outlining a method for identifying functions representing observables as vectors in Hilbert space, and in 1932, John von Neumann published follow-up papers further developing this method.
In 1931, Bernard Koopman published a paper in Proceedings of the National Academy of Sciences laying out a novel method for identifying functions representing observables on a classical system’s phase space as vectors in a Hilbert space; however, the full story of this now-ubiquitous technique, and its connection to quantum theory, reveals a complex history of attribution. John von Neumann followed up in 1932 with further development published in German Annals of Mathematics, papers that were never translated into English. As Jacob Barandes details in a new analysis, the method of “classical” wave…
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