Riesz completions, functional representations, and anti-lattices

DOI10.1007/s11117-013-0240-xzbMath1320.46016OpenAlexW2009383540MaRDI QIDQ743479

Onno van Gaans, Bas Lemmens, Anke Kalauch

Publication date: 24 September 2014

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-013-0240-x

zbMATH Keywords

embeddingfunctional representationpartially ordered vector spacedisjointnessRiesz completionanti-latticeRiesz homomorphism

Mathematics Subject Classification ID

Ordered topological linear spaces, vector lattices (46A40) Ordered normed spaces (46B40) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (11)

Projection bands and atoms in pervasive pre-Riesz spaces ⋮ Order theoretical structures in atomic JBW-algebras: disjointness, bands, and centres ⋮ Disjointness preserving \(\mathrm{C}_0\)-semigroups and local operators on ordered Banach spaces ⋮ Bands in partially ordered vector spaces with order unit ⋮ On Disjointness, Bands and Projections in Partially Ordered Vector Spaces ⋮ Multiplicative Representation of Real-Valued bi-Riesz Homomorphisms on Partially Ordered Vector Spaces ⋮ Riesz\(^*\) homomorphisms on pre-Riesz spaces consisting of continuous functions ⋮ Directed ideals in partially ordered vector spaces ⋮ Vector lattice covers of ideals and bands in Pre-Riesz spaces ⋮ Order closed ideals in pre-Riesz spaces and their relationship to bands ⋮ Operators in pre-Riesz spaces: moduli and homomorphisms

Cites Work

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• Disjointness in partially ordered vector spaces
• Ideals and bands in pre-Riesz spaces
• Ordered linear spaces
• Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions.)
• Bands in pervasive pre-Riesz spaces
• Facial Structure of Compact Convex Sets
• A Characterization of the Normed Vector Ordered Spaces of Continuous Functions Over a Compact Space
• A representation theory for commutative topological algebra
• Order Properties of Bounded Self-Adjoint Operators

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