Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
operators on Hilbert spaces
|
| gptkbp:field |
functional analysis
|
| gptkbp:formedBy |
gptkb:Paul_Halmos
1950s |
| https://www.w3.org/2000/01/rdf-schema#label |
Invariant subspace problem
|
| gptkbp:notablePartialResult |
affirmative answer for compact operators
affirmative answer for normal operators affirmative answer for some Banach spaces affirmative answer for polynomially compact operators |
| gptkbp:relatedTo |
gptkb:Hilbert_space
linear operator invariant subspace |
| gptkbp:seeAlso |
Invariant subspace theorem
Lomonosov's theorem |
| gptkbp:status |
open (as of 2024)
|
| gptkbp:type |
Does every bounded linear operator on a separable infinite-dimensional Hilbert space have a non-trivial closed invariant subspace?
|
| gptkbp:bfsParent |
gptkb:Nest_Algebras
|
| gptkbp:bfsLayer |
7
|