`BookProof.ChapterCyclicDirectSum.starProjection_cyclicSubspace_commutes` (xi : H) (g : C(spectrum ℂ T, ℂ)) : Commute (cyclicSubspace T hT xi).starProjection (cfcHom hT g)

Proved

BookProof.ChapterCyclicDirectSum.starProjection_cyclicSubspace_commutes

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCyclicDirectSum.

BookProof.ChapterCyclicDirectSum.starProjection_cyclicSubspace_commutes (xi : H) (g : C(spectrum ℂ T, ℂ)) : Commute (cyclicSubspace T hT xi).starProjection (cfcHom hT g)

Formalization note: Lean 4 identifier BookProof.ChapterCyclicDirectSum.starProjection_cyclicSubspace_commutes.

Preamble

-- Generated from ChapterCyclicDirectSum.lean — theorem BookProof.ChapterCyclicDirectSum.starProjection_cyclicSubspace_commutes
import Definitions.Def_ChapterCyclicDecomposition
import Mathlib
import Definitions.Def_ChapterCyclicDirectSum
open BookProof.ChapterCyclicDirectSum


noncomputable section

open MeasureTheory Complex


open BookProof.ChapterCyclicDecomposition

variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
variable (T : H →L[ℂ] H) (hT : IsStarNormal T)

Formal statement

theorem BookProof.ChapterCyclicDirectSum.starProjection_cyclicSubspace_commutes (xi : H) (g : C(spectrum ℂ T, ℂ)) :
    Commute (cyclicSubspace T hT xi).starProjection (cfcHom hT g) := by sorry

View graph