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there had been no references at Hilbert space, I have added the following, focusing on the origin and application in quantum mechanics:
John von Neumann, Mathematische Grundlagen der Quantenmechanik. (German) Mathematical Foundations of Quantum Mechanics. Berlin, Germany: Springer Verlag, 1932.
George Mackey, The Mathematical Foundations of Quamtum Mechanics A Lecture-note Volume, ser. The mathematical physics monograph series. Princeton university, 1963
E. Prugovecki, Quantum mechanics in Hilbert Space. Academic Press, 1971.
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