# nLab Hilbert lattice

A Hilbert lattice is the lattice of closed subspaces of a Hilbert spaces (with preorder given by the inclusion) over real, complex or quaternion numbers.

• G. Birkhoff, John von Neumann, The logic of quantum mechanics, Annals of Mathematics, 37: 823-843 (1936)

• A. Gleason, Measures on the closed subspaces of a Hilbert space, Journal of Mathematics and Mechanics 6: 885-893 (1957)

• Samuel S. Holland Jr., Orthomodularity in infinite dimensions; a theorem of M. Solèr, Bull. Amer. Math. Soc. (N.S.) 32 (1995) 205-234, arXiv:math.RA/9504224