Theorems · Definition · functional analysis

ContinuousAlternatingMap.curryLeft

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : NontriviallyNormedField 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : NormedSpace 𝕜 E] →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : NormedSpace 𝕜 F] → {n : ℕ} → E [⋀^Fin (n + 1)]→L[𝕜] F → E →L[𝕜] E [⋀^Fin n]→L[𝕜] F

Given a continuous alternating map f in n+1 variables, split the first variable to obtain a continuous linear map into continuous alternating maps in n variables, given by x ↦ (m ↦ f (Matrix.vecCons x m)). It can be thought of as a map $Hom(\bigwedge^{n+1} M, N) \to Hom(M, Hom(\bigwedge^n M, N))$. This is ContinuousMultilinearMap.curryLeft for AlternatingMap. See also ContinuousAlternatingMap.curryLeftLI.

Defined in

Mathlib.Analysis.Normed.Module.Alternating.Curry

Cited by

14 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace