`BookProof.ChapterNumericalRangeSemigroup.norm_resolvent_le` {A : E →L[ℂ] E} {ω : ℝ} (h : NumReLE A ω) {z : ℂ} (hz : ω < z.re) : ‖((shiftEquiv h hz).symm : E →L[ℂ] E)‖ ≤...

Proved

BookProof.ChapterNumericalRangeSemigroup.norm_resolvent_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNumericalRangeSemigroup.

BookProof.ChapterNumericalRangeSemigroup.norm_resolvent_le {A : E →L[ℂ] E} {ω : ℝ} (h : NumReLE A ω) {z : ℂ} (hz : ω < z.re) : ‖((shiftEquiv h hz).symm : E →L[ℂ] E)‖ ≤ (z.re - ω)⁻¹

Formalization note: Lean 4 identifier BookProof.ChapterNumericalRangeSemigroup.norm_resolvent_le.

Preamble

-- Generated from ChapterNumericalRangeSemigroup.lean — theorem BookProof.ChapterNumericalRangeSemigroup.norm_resolvent_le
import Mathlib
import Definitions.Def_ChapterNumericalRangeSemigroup
import Definitions.Def_ChapterContinuityUnitaryInfinite
open BookProof.ChapterContinuityUnitaryInfinite
open BookProof.ChapterNumericalRangeSemigroup


open scoped InnerProductSpace


variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]

Formal statement

theorem BookProof.ChapterNumericalRangeSemigroup.norm_resolvent_le {A : E →L[ℂ] E} {ω : ℝ} (h : NumReLE A ω) {z : ℂ} (hz : ω < z.re) :
    ‖((shiftEquiv h hz).symm : E →L[ℂ] E)‖ ≤ (z.re - ω)⁻¹ := by sorry

View graph