Extensions of ordering sets of states from effect algebras onto their MacNeille completions
Jiří Janda, Zdenka Riečanová · EPiC series in computing · 2018
In [Riečanová Z, Zajac M.: Hilbert Space Effect-Representations of Effect Algebras] it was shown that an effect algebra E with an ordering set M of states can by embedded into a Hilbert space effect algebra E(l2(M)). We consider the problem when its effect algebraic MacNeille completion Ê can be also embedded into the same Hilbert space effect algebra E(l2(M)). That is when the ordering set M of states on E can be be extended to an ordering set of states on Ê. We give an answer for all Archimedean MV-effect algebras and Archimedean atomic lattice effect algebras.