Traces and subadditive measures on projections in 𝐽𝐵𝑊-algebras and von Neumann algebras

Abstract

Let P ( M ) P(M) be the projection lattice of an arbitrary JBW-algebra or von Neumann algebra M. It is shown that the tracial states of M correspond by extension precisely to the subadditive probability measures on P ( M ) P(M) . The analogous result for normal semifinite traces is also proved.