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The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.

3 votes
1 answer
237 views

How much of a factor's structure is determined by the order-type of its projection lattice?

H. A. Dye showed that a type II or III factor $R$ is determined, up to *-algebraic isomorphism or anti-isomorphism, by the ortholattice-isomorphism type of its projection lattice ("ortholattice-isomor …
Doug McLellan's user avatar
5 votes
1 answer
158 views

Does every non-type-I factor's projection lattice admit a dense embedding of the standard co...

Let $R$ be a non-type-I factor acting on a separable Hilbert space. Let $P(R)$ be the set of $R$'s projections with the usual ordering ($x \leq y \iff$ range$(x) \subseteq$ range$(y)$) under which it …
Doug McLellan's user avatar
1 vote

Does every non-type-I factor's projection lattice admit a dense embedding of the standard co...

I believe I've shown (see answer to related stackoverflow question at https://math.stackexchange.com/a/4223869/250373 ) that there is such an embedding, on the supposition that every nontrivial lattic …
Doug McLellan's user avatar