Vol. 20, No. 2, 1967

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Asymptoticity and semimodularity in projection lattices

David Morris Topping

Vol. 20 (1967), No. 2, 317–325
Abstract

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
Milestones
Received: 21 February 1966
Published: 1 February 1967
Authors
David Morris Topping