Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
sequence space
|
| gptkbp:alsoKnownAs |
lp space
|
| gptkbp:category |
topological vector space
|
| gptkbp:complete |
true
|
| gptkbp:contains |
all sequences (x_n) such that Σ |x_n|^p < ∞
|
| gptkbp:containsElement |
sequence of real or complex numbers
|
| gptkbp:definedIn |
1 ≤ p < ∞
|
| gptkbp:hasDual |
l^q (where 1/p + 1/q = 1, 1 < p < ∞)
|
| gptkbp:hasNorm |
l^p norm
|
| gptkbp:hasSpecialCase |
l^2 is a Hilbert space
|
| gptkbp:hasSubgroup |
all sequences
|
| https://www.w3.org/2000/01/rdf-schema#label |
sequence space l^p
|
| gptkbp:introduced |
gptkb:David_Hilbert
|
| gptkbp:isBanachSpace |
true
|
| gptkbp:isNotReflexive |
true (for p = 1 or p = ∞)
|
| gptkbp:isReflexive |
true (for 1 < p < ∞)
|
| gptkbp:isSeparable |
true (for 1 ≤ p < ∞)
|
| gptkbp:isVectorSpace |
true
|
| gptkbp:normDefinedAs |
(Σ |x_n|^p)^{1/p}
|
| gptkbp:relatedTo |
sequence space l^∞
|
| gptkbp:usedIn |
gptkb:probability_theory
gptkb:signal_processing Fourier analysis functional analysis |
| gptkbp:bfsParent |
gptkb:Lebesgue_space
|
| gptkbp:bfsLayer |
6
|