7 papers
The sup-inf-completion of a Dedekind complete vector lattice
Eder Kikianty, Luan Naude, Mark Roelands +1
We introduce the sup-inf-completion of a Dedekind complete vector lattice, an essentially unique extension in which every nonempty subset has both a supremum and an infimum. Since…
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…
The Riemann integral on Dedekind complete -algebras
Eder Kikianty, Luan Naude, Mark Roelands +1
In this paper we develop a theory of integration for locally band preserving functions, introduced by Ercan and Wickstead, on Dedekind complete -algebras. Specifically, we const…
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…
Classical theorems from analysis for locally band preserving functions on Dedekind complete -algebras
Eder Kikianty, Luan Naude, Mark Roelands +1
In this paper we explore the concept of locally band preserving functions, introduced by Ercan and Wickstead, on Dedekind complete -algebras. Specifically, we show that all sup…
Infinite dimensional symmetric cones and gauge-reversing maps
Bas Lemmens, Mark Roelands, Marten Wortel
The famous Koecher-Vinberg theorem characterises the finite dimensional formally real Jordan algebras among the finite dimensional order unit spaces as the ones that have a symmetr…