Theorems · Theorem · functional analysis

ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {n : ℕ} (f : F [⋀^Fin n]→L[𝕜] G) (g : E →L[𝕜] F)
  {h : E →L[𝕜] E →L[𝕜] F},
  (∀ (x y : E), (h x) y = (h y) x) →
    ContinuousAlternatingMap.alternatizeUncurryFin (f.fderivCompContinuousLinearMap g ∘SL h) = 0

alternatizeUncurryFin of fderivCompContinuousLinearMap f g composed with a symmetric bilinear map is zero.

Defined in

Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin

Cited by

1 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace