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Topological Orthoalgebras | | Alexander Wilce
; | | Date: |
8 Dec 2002 | | Subject: | Rings and Algebras; General Topology MSC-class: 03G12; 06C15; 06F30; 54H12 | math.RA math.GN quant-ph | | Abstract: | We define topological orthoalgebras (TOAs) and study their properties. While every topological orthomodular lattice is a TOA, the lattice of projections of a Hilbert space is an example of a lattice-ordered TOA that is not a toplogical lattice. On the other hand, we show that every compact Boolean TOA is a topological Boolean algebra. We also show that a compact TOA in which 0 is an isolated point is atomic and of finite height. We identify and study a particularly tractable class of TOAs, which we call {em stably ordered}: those in which the upper-set generated by an open set is open. This includes all topological OMLs, and also the projection lattices of Hilbert spaces. Finally, we obtain a topological version of the Foulis-Randall representation theory for stably ordered TOAs | | Source: | arXiv, math.RA/0301072 | | Services: | Forum | Review | PDF | Favorites | |
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