Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:alsoKnownAs |
vector lattice
|
| gptkbp:application |
gptkb:Banach_lattice_theory
measure theory operator theory |
| gptkbp:category |
ordered vector spaces
|
| gptkbp:definedIn |
vector space equipped with a lattice order
|
| gptkbp:example |
L^p spaces for 1 ≤ p ≤ ∞
space of real-valued continuous functions on a compact space |
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:generalizes |
function spaces with pointwise order
real numbers as an ordered vector space |
| gptkbp:hasAxiom |
if x ≤ y then x + z ≤ y + z
if x ≤ y then αx ≤ αy for all α ≥ 0 supremum and infimum exist for every pair of elements |
| gptkbp:hasSubfield |
functional analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riesz spaces
|
| gptkbp:namedAfter |
gptkb:Frigyes_Riesz
|
| gptkbp:property |
order structure compatible with vector space operations
|
| gptkbp:relatedTo |
gptkb:Banach_lattices
order complete vector spaces |
| gptkbp:bfsParent |
gptkb:Banach_lattice_theory
|
| gptkbp:bfsLayer |
7
|