Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Hilbert_space
sequence space |
| gptkbp:basisFor |
standard basis (sequences with 1 in one position, 0 elsewhere)
|
| gptkbp:category |
topological vector space
|
| gptkbp:complete |
true
|
| gptkbp:contains |
all sequences (x_n) with sum |x_n|^2 < ∞
|
| gptkbp:definedIn |
set of all square-summable sequences
|
| gptkbp:dimensions |
countably infinite
|
| gptkbp:field |
complex numbers
real numbers |
| gptkbp:hasDual |
itself
|
| gptkbp:hasSubgroup |
gptkb:l^p_space
|
| https://www.w3.org/2000/01/rdf-schema#label |
l^2 space
|
| gptkbp:innerProductDefinedBy |
sum of products of sequence elements
|
| gptkbp:isBanachSpace |
true
|
| gptkbp:normDefinedBy |
square root of sum of squares
|
| gptkbp:notation |
l^2
ℓ² |
| gptkbp:separates |
true
|
| gptkbp:usedIn |
functional analysis
quantum mechanics |
| gptkbp:bfsParent |
gptkb:l^p_space
|
| gptkbp:bfsLayer |
5
|