4 papers
Order convergence in ordered vector spaces: compactness, atoms, pervasiveness, and ice cream spaces
Eugene Bilokopytov, Mark Roelands, Samuel Tiersma +3
We study order convergence in ordered vector spaces that are not necessarily lattices. In this setting, we consider two generalizations of order convergence on vector lattices, a d…
On the Shirshov--Cohn theorem for JB-algebras
Mark Roelands, Samuel Tiersma
It is shown that a JB-algebra which can be generated by the union of two of its associative Jordan subalgebras is a JC-algebra, hence special. A similar refinement of Macdonald's p…
An order-theoretic characterization of C*-algebras
Samuel Tiersma
We give an order-theoretic characterization of the essential image of the forgetful functor from the category of real/complex unital C*-algebras to the category of real/complex uni…
An order-theoretic characterization of JB-algebras
Mark Roelands, Samuel Tiersma
We give an order-theoretic characterization of the JB-algebras among the complete order unit spaces in terms of the existence of an order-anti-automorphism of the interior of the c…