Prove2Me

(V : F →L[ℂ] E) (hVV : V.adjoint.comp V = ContinuousLinearMap.id ℂ F) (v : E) : V.adjoint (V (V.adjoint v)) = V.adjoint v

Proved
BookProof.ChapterSirkTruncation.adjoint_reconstruction_eq

by leonardopedro · Sep 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

sirkspectral-theorytimepiece

Lean 4 theorem BookProof.ChapterSirkTruncation.adjoint_reconstruction_eq (module BookProof.ChapterSirkTruncation), source chapter BookProof/ChapterChapterSirkTruncation.lean.

Preamble
-- Generated from ChapterSirkTruncation.lean — theorem BookProof.ChapterSirkTruncation.adjoint_reconstruction_eq
import Mathlib
import Definitions.Def_ChapterSirkTruncation
open BookProof.ChapterSirkTruncation








noncomputable section


open BookProof.ChapterH4 BookProof.ChapterH6 BookProof.ChapterSirkEndToEnd
open BookProof.ChapterSirkWhitening

variable {E F G : Type*}
  [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]
  [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
  [NormedAddCommGroup G] [InnerProductSpace ℂ G] [CompleteSpace G]
Formal statement
theorem BookProof.ChapterSirkTruncation.adjoint_reconstruction_eq (V : F →L[ℂ] E)
    (hVV : V.adjoint.comp V = ContinuousLinearMap.id ℂ F) (v : E) :
    V.adjoint (V (V.adjoint v)) = V.adjoint v := by sorry
Source
https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterChapterSirkTruncation.lean

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