Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Hilbert_space
function space |
| gptkbp:category |
gptkb:normed_vector_space
sequence space |
| gptkbp:complete |
true
|
| gptkbp:contains |
l^q space for q > p
|
| gptkbp:definedIn |
sequence of real or complex numbers
|
| gptkbp:defines |
set of all sequences (x_n) such that sum |x_n|^p < ∞
|
| gptkbp:generalizes |
gptkb:l^1_space
gptkb:l^2_space l^∞ space (as p → ∞) |
| gptkbp:hasDual |
l^q space for 1/p + 1/q = 1, p > 1
|
| gptkbp:hasSpecialCase |
l^2 space is a Hilbert space
|
| gptkbp:hasSubgroup |
all sequences
|
| https://www.w3.org/2000/01/rdf-schema#label |
l^p space for p ≥ 1
|
| gptkbp:norm |
p-norm
|
| gptkbp:notation |
l^p
ℓ^p |
| gptkbp:parameter |
p ≥ 1
|
| gptkbp:reflexive |
true for 1 < p < ∞
|
| gptkbp:separates |
true for p < ∞
|
| gptkbp:studiedBy |
gptkb:David_Hilbert
|
| gptkbp:usedIn |
gptkb:probability_theory
gptkb:signal_processing functional analysis mathematical analysis |
| gptkbp:bfsParent |
gptkb:l^1_space
|
| gptkbp:bfsLayer |
6
|