Theorems · Theorem · functional analysis

ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply

∀ (𝕜 : Type u) {ι : Type v} (E : ι → Type wE) (E₁ : ι → Type wE₁) (G : Type wG) [inst : NontriviallyNormedField 𝕜]
  [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)]
  [inst_3 : (i : ι) → SeminormedAddCommGroup (E₁ i)] [inst_4 : (i : ι) → NormedSpace 𝕜 (E₁ i)]
  [inst_5 : SeminormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] [inst_7 : Fintype ι] (f : (i : ι) → E i →L[𝕜] E₁ i)
  (g : ContinuousMultilinearMap 𝕜 E₁ G),
  ((ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear 𝕜 E E₁ G) f) g = g.compContinuousLinearMap f

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Basic

Cited by

2 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceFintype