5 papers
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…
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…
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…
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…
Artinian and Noetherian vector lattices
Marko KandiÄ, 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…