Prove2Me

`BookProof.ChapterSchurRepresentation.adjoint_uCLM` (f : V ≃ₗᵢ[ℂ] V) : ContinuousLinearMap.adjoint (uCLM f) = uCLM f.symm

Proved
BookProof.ChapterSchurRepresentation.adjoint_uCLM

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSchurRepresentation.

BookProof.ChapterSchurRepresentation.adjoint_uCLM (f : V ≃ₗᵢ[ℂ] V) : ContinuousLinearMap.adjoint (uCLM f) = uCLM f.symm

Formalization note: Lean 4 identifier BookProof.ChapterSchurRepresentation.adjoint_uCLM.

Preamble
-- Generated from ChapterSchurRepresentation.lean — theorem BookProof.ChapterSchurRepresentation.adjoint_uCLM
import Definitions.Def_ChapterA
import Definitions.Def_ChapterSchurIrreducible
import Mathlib
import Definitions.Def_ChapterSchurRepresentation
open BookProof.ChapterSchurRepresentation


open scoped ComplexConjugate InnerProductSpace


open BookProof.ChapterA BookProof.ChapterA.System BookProof.ChapterSchurIrreducible

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]
Formal statement
theorem BookProof.ChapterSchurRepresentation.adjoint_uCLM (f : V ≃ₗᵢ[ℂ] V) :
    ContinuousLinearMap.adjoint (uCLM f) = uCLM f.symm := by sorry

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