Eigenspaces of continuous linear maps #
This file provides some basic properties of eigenspaces of continuous linear maps.
These results are in a separate file to avoid heavy topology imports.
instance
ContinuousLinearMap.isClosed_genEigenspace
{R : Type u_1}
{M : Type u_2}
[CommRing R]
[AddCommGroup M]
[Module R M]
[TopologicalSpace M]
[T0Space M]
[ContinuousConstSMul R M]
[IsTopologicalAddGroup M]
(f : M →L[R] M)
(μ : R)
(n : ℕ)
:
IsClosed ↑((Module.End.genEigenspace (↑f) μ) ↑n)
instance
ContinuousLinearMap.isClosed_eigenspace
{R : Type u_1}
{M : Type u_2}
[CommRing R]
[AddCommGroup M]
[Module R M]
[TopologicalSpace M]
[T0Space M]
[ContinuousConstSMul R M]
[IsTopologicalAddGroup M]
(f : M →L[R] M)
(μ : R)
:
IsClosed ↑(Module.End.eigenspace (↑f) μ)