10 citations · 23 across the 15 of their papers we have counts for
20 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 Riesz-Kantorovich formulas for -vector lattices
Tomas Chamberlain, Marten Wortel
Let be a Dedekind complete unital -algebra. We prove the Riesz-Kantorovich formulas for order bounded -module homomorphisms from a directed partially or…
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-valued integration
Xingni Jiang, Jan Harm van der Walt, Marten Wortel
We develop integration theory for integrating functions taking values into a Dedekind complete unital -algebra with respect to -valued measures. We then…
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 isomorphisms on order intervals of atomic JBW-algebras
Mark Roelands, Marten Wortel
In this paper a full description of order isomorphisms between effect algebras of atomic JBW-algebras is given. We will derive a closed formula for the order isomorphisms on the ef…
Lexicographic cones and the ordered projective tensor product
Marten Wortel
We introduce lexicographic cones, a method of assigning an ordered vector space $\Lex(S)$ to a poset , generalising the standard lexicographic cone. These lexicographic cones ar…
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…
Hilbert isometries and maximal deviation preserving maps on JB-algebras
Mark Roelands, Marten Wortel
In this paper we characterize the surjective linear variation norm isometries on JB-algebras. Variation norm isometries are precisely the maps that preserve the maximal deviation,…
Riesz-Kantorovich formulas for operators on multi-wedged spaces
Christopher Schwanke, Marten Wortel
We introduce the notions of multi-suprema and multi-infima for vector spaces equipped with a collection of wedges, generalizing the notions of suprema and infima in ordered vector…
Hilbert and Thompson isometries on cones in JB-algebras
Bas Lemmens, Mark Roelands, Marten Wortel
Hilbert's and Thompson's metric spaces on the interior of cones in JB-algebras are important examples of symmetric Finsler spaces. In this paper we characterize the Hilbert's metri…
The intrinsic metric on the unit sphere of a normed space
Miek Messerschmidt, Marten Wortel
Let denote the unit sphere of a real normed space. We show that the intrinsic metric on is strongly equivalent to the induced metric on . Specifically, for all $x,y\in S…
Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces
Bas Lemmens, Brian Lins, Roger Nussbaum +1
We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert's metric or Thompson's m…
Isometries of infinite dimensional Hilbert geometries
Bas Lemmens, Mark Roelands, Marten Wortel
In this paper we extend results by De la Harpe concerning the isometries of strictly convex Hilbert geometries, and the characterisation of the isometry groups of Hilbert geometrie…
Crossed products of Banach algebras. II
Marcel de Jeu, Miek Messerschmidt, Marten Wortel
In earlier work a crossed product of a Banach algebra was constructed from a Banach algebra dynamical system and a class of continuous covariant representat…
Compact groups of positive operators on Banach lattices
Marcel de Jeu, Marten Wortel
In this paper we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic imag…
Positive representations of finite groups in Riesz spaces
Marcel de Jeu, Marten Wortel
In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite group…
Crossed products of Banach algebras. I
Sjoerd Dirksen, Marcel de Jeu, Marten Wortel
We construct a crossed product Banach algebra from a Banach algebra dynamical system and a given uniformly bounded class of continuous covariant Banach space represen…
Extending representations of normed algebras in Banach spaces
Sjoerd Dirksen, Marcel de Jeu, Marten Wortel
Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this r…