Remarks on the classification problem for infinite-dimensional Hilbert lattices

Morash, Ronald P.

doi:10.1090/S0002-9939-1974-0404072-4

Remarks on the classification problem for infinite-dimensional Hilbert lattices
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Proc. Amer. Math. Soc. 43 (1974), 42-46 Request permission

Abstract:

A lattice satisfying the properties of a Hilbert lattice, but possibly reducible, possesses the relative center property. The division ring with involution $(D,\ast )$, which coordinatizes a Hilbert lattice satisfying the angle-bisection axiom and having infinite dimension, is formally real with respect to the involution, in particular having characteristic zero. Also $D$ has the property that finite sums of elements of the form $\alpha {\alpha ^\ast }$ are of the form $\beta {\beta ^\ast }$ for some $\beta \in D$.

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Remarks on Type

Baer and Baer $\ast$-rings

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