Murray-von Neumann equivalence — 1 results found.

A new structural result in the comparison theory of projections for von Neumann algebras is proved: two monotone-increasing nets of projections indexed by the same directed set have unions that are equivalent when pairs of projections with the same index are equivalent. The same is not true, in general, for intersections of monotone-decreasing nets of projections. Counterexamples are given indicating limitations on extensions, variants, and methods for proving that result.