`BookProof.ChapterCompactCompleteReducibility.continuous_conjOp` {ρ : G →* (V ≃L[ℂ] V)} (hρ : Continuous fun g => (ρ g : V →L[ℂ] V)) (T : V →L[ℂ] V) : Continuous (conjOp ρ T)
ProvedBookProof.ChapterCompactCompleteReducibility.continuous_conjOptheoremstimepiece
Prove the following Lean 4 theorem from ChapterCompactCompleteReducibility.
BookProof.ChapterCompactCompleteReducibility.continuous_conjOp {ρ : G →* (V ≃L[ℂ] V)} (hρ : Continuous fun g => (ρ g : V →L[ℂ] V)) (T : V →L[ℂ] V) : Continuous (conjOp ρ T)
Formalization note: Lean 4 identifier BookProof.ChapterCompactCompleteReducibility.continuous_conjOp.
Preamble
-- Generated from ChapterCompactCompleteReducibility.lean — theorem BookProof.ChapterCompactCompleteReducibility.continuous_conjOp
import Mathlib
import Definitions.Def_ChapterCompactCompleteReducibility
open BookProof.ChapterCompactCompleteReducibility
open MeasureTheory
variable {G : Type*} [Group G] [TopologicalSpace G] [IsTopologicalGroup G] [CompactSpace G]
[MeasurableSpace G] [BorelSpace G] {μ : Measure G} [IsProbabilityMeasure μ]
[μ.IsMulLeftInvariant]
variable {V : Type*} [NormedAddCommGroup V] [NormedSpace ℂ V] [FiniteDimensional ℂ V]
omit [CompactSpace G] [MeasurableSpace G] [BorelSpace G] [FiniteDimensional ℂ V] inFormal statement
theorem BookProof.ChapterCompactCompleteReducibility.continuous_conjOp {ρ : G →* (V ≃L[ℂ] V)}
(hρ : Continuous fun g => (ρ g : V →L[ℂ] V)) (T : V →L[ℂ] V) :
Continuous (conjOp ρ T) := by sorry