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Asymptoticity and
semimodularity in projection lattices
David Morris Topping |
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Vol. 20 (1967), No. 2, 317–325
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Abstract |
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In this note it is shown that every von Neumann algebra has a semimodular projection lattice. The notions of a dual modular pair of projections and nonasymptoticity, which were shown by Mackey to coincide in a type I∞ factor, are compared globally. A von Neumann algebra containing no asymptotic pairs of projections is characterized as the direct-sum of an abelian algebra and a finitedimensional algebra. |
Mathematical Subject Classification
Primary: 46.65
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Milestones
Received: 21 February 1966
Published: 1 February 1967
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Authors |
| David Morris Topping | |
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