In 1843 quaternions were discovered by Rowan Hamilton.
 Quantum logic was introduced by Garret Birkhoff and John von Neumann in their paper: Birkhoff, G. and von Neumann, J. (1936) The Logic of Quantum Mechanics. Annals of Mathematics, 37, 823-843.
This paper also indicates the relation between this orthomodular lattice and separable Hilbert spaces.
 The Hilbert space was discovered in the first decades of the 20th century by David Hilbert and others.
 In the sixties Israel Gelfand and GeorgyiShilov introduced a way to model continuums via an extension of the separable Hilbert space into a so called Gelfand triple. The Gelfand triple often gets the name rigged Hilbert space. It is a non-separable Hilbert space.
 Paul Dirac introduced the braket notation, which popularized the usage of Hilbert spaces. Dirac also introduced its delta function, which is a generalized function. Spaces of generalized functions offered continuums before the Gelfand triple arrived.
See: Dirac, P.A.M. (1958) The Principles of Quantum Mechanics. 4th Edition, Oxford University Press, Oxford, ISBN 978 0 19 852011 5.
 Quaternionic function theory and quaternionic Hilbert spaces are treated in: van Leunen, J.A.J. (2015) Quaternions and Hilbert Spaces.
 In the second half of the twentieth century Constantin Piron and Maria Pia Solèr proved that the number systems that a separable Hilbert space can use must be division rings. See: Baez, J. (2011) Division Algebras and Quantum Theory.
http://arxiv.org/abs/1101.5690 and Holland, S.S. (1995) Orthomodularity in Infinite Dimensions: A Theorem of M. Solèr. Bulletin of the American Mathematical Society, 32, 205-234
 van Leunen, J.A.J. (2015) Foundation of a Mathematical Model of Physical Reality.