3 citations · 3 across the 12 of their papers we have counts for
13 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…
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…
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 supe…
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…
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…
Artinian and Noetherian vector lattices
Marko Kandić, Mark Roelands, Marten Wortel
In this paper, we study Artinian and Noetherian properties in vector lattices and provide a concrete representation of these spaces. Furthermore, we describe for which Archimedean…
L-functional analysis
Eder Kikianty, Miek Messerschmidt, Luan Naude +5
Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars or $\mathbb…
Order theoretical structures in atomic JBW-algebras: disjointness, bands, and centres
Onno van Gaans, Anke Kalauch, Mark Roelands
Every atomic JBW-algebra is known to be a direct sum of JBW-algebra factors of type I. Extending Kadison's anti-lattice theorem, we show that each of these factors is a disjointnes…
Differentiable, Holomorphic, and Analytic Functions on Complex -Algebras
Mark Roelands, Christopher Michael Schwanke
Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex -algebras. Most notably, we improve the Cauc…
Equivalence after extension and Schur coupling do not coincide, on essentially incomparable Banach spaces
Sanne ter Horst, Miek Messerschmidt, Andre C. M. Ran +1
In 1994 H. Bart and V.É. Tsekanovskii posed the question whether the Banach space operator relations matricial coupling (MC), equivalence after extension (EAE) and Schur coupling (…
Equivalence after extension and Schur coupling coincide for inessential operators
S. ter Horst, M. Messerschmidt, A. C. M. Ran +2
In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operato…