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For questions about mathematical problems arising from quantum mechanics, a branch of physics describing the behaviour of nature at very small scales, at the level of atoms and subatomic particles.
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When does an orthomodular projection lattice have a non-trivial centre?
When does an orthomodular lattice $L$ of projections onto a given Hilbert space have a non-trivial centre $Z(L)$ and what can we generally say about the cardinality of $Z(L)$?
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Cardinality of the set of Boolean subalgebras of the lattice of projections on a Hilbert space
I have a simple question I've managed to get myself quite confused about.
Given a Hilbert space H, what do we know about the cardinality of
(a) the set $P(H)$ of projection operators onto $H$ (equi …