(V : F →L[ℂ] E) (X : E →L[ℂ] E) (hViso : ∀ x : F, ‖V x‖ = ‖x‖) : (convexHull ℝ) (numRange (compress V X)) ⊆ Metric.closedBall (0 : ℂ) ‖X‖
ProvedBookProof.ChapterSirkEndToEnd.crouzeix_domain_uniformsirkspectral-theorytimepiece
Lean 4 theorem BookProof.ChapterSirkEndToEnd.crouzeix_domain_uniform (module BookProof.ChapterSirkEndToEnd), source chapter BookProof/ChapterChapterSirkEndToEnd.lean.
Preamble
-- Generated from ChapterSirkEndToEnd.lean — theorem BookProof.ChapterSirkEndToEnd.crouzeix_domain_uniform
import Mathlib
import Definitions.Def_ChapterSirkEndToEnd
open BookProof.ChapterSirkEndToEnd
noncomputable section
open Filter Topology
open BookProof.ChapterH4 BookProof.ChapterH6 BookProof.ChapterH8 BookProof.ChapterH9
variable {E F : Type*}
[NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]
[NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]Formal statement
theorem BookProof.ChapterSirkEndToEnd.crouzeix_domain_uniform (V : F →L[ℂ] E) (X : E →L[ℂ] E)
(hViso : ∀ x : F, ‖V x‖ = ‖x‖) :
(convexHull ℝ) (numRange (compress V X)) ⊆ Metric.closedBall (0 : ℂ) ‖X‖ := by sorrySource