Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
class of operators
|
| gptkbp:characterizedBy |
finite Hilbert-Schmidt norm
|
| gptkbp:closed |
addition
scalar multiplication adjoint |
| gptkbp:compact |
true
|
| gptkbp:definedIn |
gptkb:Hilbert_space
|
| gptkbp:form |
gptkb:Hilbert_space
two-sided *-ideal |
| gptkbp:generalizes |
finite-rank operators
|
| gptkbp:hasInnerProduct |
trace inner product
|
| gptkbp:hasSpecialCase |
Schatten class operators
|
| gptkbp:hasSubgroup |
compact operators
bounded operators |
| https://www.w3.org/2000/01/rdf-schema#label |
Hilbert-Schmidt operators
|
| gptkbp:isIdealOf |
bounded operators
|
| gptkbp:isTraceClass |
false (in general)
|
| gptkbp:namedAfter |
gptkb:David_Hilbert
gptkb:Erhard_Schmidt |
| gptkbp:normDefinedBy |
sum of squares of singular values
trace of T*T |
| gptkbp:numberOfIssues |
true
|
| gptkbp:SchattenClassIndex |
2
|
| gptkbp:usedIn |
functional analysis
operator theory quantum mechanics |
| gptkbp:bfsParent |
gptkb:Mercer's_theorem
|
| gptkbp:bfsLayer |
6
|