Riesz spacevalued states on pseudo MValgebras
Abstract
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. Besides 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 DOI:
 10.48550/arXiv.1709.06502
 arXiv:
 arXiv:1709.06502
 Bibcode:
 2017arXiv170906502D
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Functional Analysis;
 06D35;
 06C15