 Riesz SpaceValued States on Pseudo MValgebras
Anatolij Dvurev{c}enskij
We introduce Riesz spacevalued states, called $(R,1_R)$states, on a pseudo MValgebra, where $R$ is a Riesz space with a fixed strong unit $1_R$. Pseudo MValgebras are a noncommutative generalization of MValgebras. Such a Riesz spacevalued state is a generalization of usual states on MValgebras. Any $(R,1_R)$state is an additive mapping preserving a partial addition in pseudo MValgebras. We introduce $(R,1_R)$statemorphisms and extremal $(R,1_R)$states, and we study relations between them. We study metrical completion of unital $ell$groups with respect to an $(R,1_R)$state. If the unital Riesz space is Dedekind complete, we study when the space of $(R,1_R)$states is a Choquet simplex or even a Bauer simplex.
