12 citations · 19 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
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…
On the linearity of order-isomorphisms
Bas Lemmens, Hent van Imhoff, Onno van Gaans
A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every…
Disjointness preserving -semigroups and local operators on ordered Banach spaces
Anke Kalauch, Onno van Gaans, Feng Zhang
We generalize results concerning -semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving $\math…
Bands in partially ordered vector spaces with order unit
Anke Kalauch, Bas Lemmens, Onno van Gaans
In an Archimedean directed partially ordered vector space one can define the concept of a band in terms of disjointness. Bands can be studied by using a vector lattice cover $Y…
Dissipativity of the delay semigroup
Joris Bierkens
Under mild conditions a delay semigroup can be transformed into a (generalized) contraction semigroup by modifying the inner product on the (Hilbert) state space into an equivalent…