`BookProof.KatoRellich.essentiallySelfAdjointOn_add_bounded` [CompleteSpace F] (H : D →ₗ[ℂ] F) (hH : SymmetricOn D H) (hesa : EssentiallySelfAdjointOn D H) (B : F →L[ℂ] F) (hB : ∀

Proved

BookProof.KatoRellich.essentiallySelfAdjointOn_add_bounded

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterKatoRellichDeficiency.

BookProof.KatoRellich.essentiallySelfAdjointOn_add_bounded [CompleteSpace F] (H : D →ₗ[ℂ] F) (hH : SymmetricOn D H) (hesa : EssentiallySelfAdjointOn D H) (B : F →L[ℂ] F) (hB : ∀ x y : F, (inner ℂ (B x) y : ℂ) = inner ℂ x (B y)) : EssentiallySelfAdjointOn D (H + (B.toLinearMap ∘ₗ D.subtype))

Formalization note: Lean 4 identifier BookProof.KatoRellich.essentiallySelfAdjointOn_add_bounded.

Preamble

-- Generated from ChapterKatoRellichDeficiency.lean — theorem BookProof.KatoRellich.essentiallySelfAdjointOn_add_bounded
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterKatoRellichDeficiency
import Definitions.Def_ChapterFarisLavineCore



open BookProof.FarisLavine

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}

Formal statement

theorem BookProof.KatoRellich.essentiallySelfAdjointOn_add_bounded [CompleteSpace F] (H : D →ₗ[ℂ] F)
    (hH : SymmetricOn D H) (hesa : EssentiallySelfAdjointOn D H) (B : F →L[ℂ] F)
    (hB : ∀ x y : F, (inner ℂ (B x) y : ℂ) = inner ℂ x (B y)) :
    EssentiallySelfAdjointOn D (H + (B.toLinearMap ∘ₗ D.subtype)) := by sorry

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