Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
class of operators
|
| gptkbp:application |
quantum mechanics
integral equations |
| gptkbp:characterizedBy |
finite Hilbert–Schmidt norm
|
| gptkbp:definedIn |
gptkb:Hilbert_space
|
| gptkbp:example |
integral operator with square-integrable kernel
|
| gptkbp:field |
functional analysis
operator theory |
| gptkbp:generalizes |
finite-rank operators
trace-class operators |
| https://www.w3.org/2000/01/rdf-schema#label |
Hilbert–Schmidt operators
|
| gptkbp:introduced |
early 20th century
|
| gptkbp:namedAfter |
gptkb:David_Hilbert
gptkb:Erhard_Schmidt |
| gptkbp:norm |
gptkb:Hilbert–Schmidt_norm
|
| gptkbp:notation |
HS(H)
|
| gptkbp:property |
compactness
closed under addition closed under adjoint operation closed under scalar multiplication form a Hilbert space ideal in bounded operators not closed under composition self-adjoint if operator equals its adjoint separable Hilbert space |
| gptkbp:subset_of |
compact operators
bounded operators |
| gptkbp:used_in |
gptkb:Fredholm_theory
random matrix theory spectral theory |
| gptkbp:bfsParent |
gptkb:Hilbert–Schmidt_norm
|
| gptkbp:bfsLayer |
7
|