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

Bunce, L. J.; Hamhalter, J.

doi:10.1090/S0002-9939-1995-1223512-8

Traces and subadditive measures on projections in $\textrm {JBW}$-algebras and von Neumann algebras
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by L. J. Bunce and J. Hamhalter PDF

Proc. Amer. Math. Soc. 123 (1995), 157-160 Request permission

Abstract:

Let $P(M)$ 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 $P(M)$. The analogous result for normal semifinite traces is also proved.

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