Theorems · Theorem · functional analysis

LinearMap.extendOfNorm.congr_simp

∀ {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_3} {Eₗ : Type u_4} {F : Type u_5} [inst : NormedDivisionRing 𝕜]
  [inst_1 : NormedDivisionRing 𝕜₂] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_2 : AddCommGroup E] [inst_3 : SeminormedAddCommGroup Eₗ]
  [inst_4 : NormedAddCommGroup F] [inst_5 : Module 𝕜 E] [inst_6 : Module 𝕜₂ F] [inst_7 : IsBoundedSMul 𝕜₂ F]
  [inst_8 : Module 𝕜 Eₗ] [inst_9 : IsBoundedSMul 𝕜 Eₗ] [inst_10 : CompleteSpace F] (f f_1 : E →ₛₗ[σ₁₂] F),
  f = f_1 → ∀ (e e_1 : E →ₗ[𝕜] Eₗ), e = e_1 → f.extendOfNorm e = f_1.extendOfNorm e_1

Defined in

Mathlib.Analysis.Normed.Operator.Extend

Cited by

0 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedDivisionRingNormedDivisionRingAddCommGroupSeminormedAddCommGroupNormedAddCommGroupModuleModuleIsBoundedSMulModuleIsBoundedSMulCompleteSpace