`BookProof.ChapterAbelianDiagonalCountable.commutes_diagOp_iff` (T : Ell2C →L[ℂ] Ell2C) : (∀ d : EllInf, T.comp (diagOp d) = (diagOp d).comp T) ↔ ∃ d : EllInf, T = diagOp d

Proved

BookProof.ChapterAbelianDiagonalCountable.commutes_diagOp_iff

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianDiagonalCountable.

BookProof.ChapterAbelianDiagonalCountable.commutes_diagOp_iff (T : Ell2C →L[ℂ] Ell2C) : (∀ d : EllInf, T.comp (diagOp d) = (diagOp d).comp T) ↔ ∃ d : EllInf, T = diagOp d

Formalization note: Lean 4 identifier BookProof.ChapterAbelianDiagonalCountable.commutes_diagOp_iff.

Preamble

-- Generated from ChapterAbelianDiagonalCountable.lean — theorem BookProof.ChapterAbelianDiagonalCountable.commutes_diagOp_iff
import Mathlib
import Definitions.Def_ChapterAbelianDiagonalCountable
open BookProof.ChapterAbelianDiagonalCountable


open scoped ENNReal

noncomputable section

Formal statement

theorem BookProof.ChapterAbelianDiagonalCountable.commutes_diagOp_iff (T : Ell2C →L[ℂ] Ell2C) :
    (∀ d : EllInf, T.comp (diagOp d) = (diagOp d).comp T) ↔ ∃ d : EllInf, T = diagOp d := by sorry

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