Theorems · Definition · functional analysis

ContinuousMultilinearMap.curryRight

{𝕜 : Type u} →
  {n : ℕ} →
    {Ei : Fin n.succ → Type wEi} →
      {G : Type wG} →
        [inst : NontriviallyNormedField 𝕜] →
          [inst_1 : (i : Fin n.succ) → NormedAddCommGroup (Ei i)] →
            [inst_2 : (i : Fin n.succ) → NormedSpace 𝕜 (Ei i)] →
              [inst_3 : NormedAddCommGroup G] →
                [inst_4 : NormedSpace 𝕜 G] →
                  ContinuousMultilinearMap 𝕜 Ei G → Ei i.castSucc [×n]→L[𝕜] Ei (Fin.last n) →L[𝕜] G

Given a continuous multilinear map f in n+1 variables, split the last variable to obtain a continuous multilinear map in n variables into continuous linear maps, given by m ↦ (x ↦ f (snoc m x)).

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Curry

Cited by

5 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace