Theorems · Definition · functional analysis

ContinuousMultilinearMap.uncurryRight

{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] →
                  (Ei i.castSucc [×n]→L[𝕜] Ei (Fin.last n) →L[𝕜] G) → ContinuousMultilinearMap 𝕜 Ei G

Given a continuous linear map f from continuous multilinear maps on n variables to continuous linear maps on E 0, construct the corresponding continuous multilinear map on n+1 variables obtained by concatenating the variables, given by m ↦ f (init m) (m (last n)).

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Curry

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace