Asymptoticity and semimodularity in projection lattices
David M. Topping · Pacific Journal of Mathematics · 1967
In this note it is shown that every von Neumann algebra has a semi modular 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.