Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Hilbert_space
gptkb:algebra vector lattice |
| gptkbp:definedIn |
a real or complex Banach space that is also a vector lattice such that the norm is compatible with the lattice operations
|
| gptkbp:example |
gptkb:L^p_spaces_(1_≤_p_≤_∞)
C(K) spaces (continuous functions on compact Hausdorff space K) |
| gptkbp:field |
gptkb:mathematics
functional analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Banach lattice
|
| gptkbp:introduced |
gptkb:G._Birkhoff
|
| gptkbp:property |
the norm satisfies |x| ≤ |y| implies ||x|| ≤ ||y||
the lattice operations are continuous with respect to the norm |
| gptkbp:relatedConcept |
gptkb:Riesz_space
order unit positive operator |
| gptkbp:used_in |
gptkb:probability_theory
ergodic theory mathematical analysis measure theory theory of positive operators |
| gptkbp:bfsParent |
gptkb:Riesz_space
|
| gptkbp:bfsLayer |
6
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