Theorems · Definition · functional analysis

ContinuousMultilinearMap.curryLeft

{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 0 →L[𝕜] Ei i.succ [×n]→L[𝕜] G

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

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Curry

Cited by

27 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace