Theorems · Definition · functional analysis

ContinuousMultilinearMap.fderivCompContinuousLinearMap

{𝕜 : Type u} →
  {ι : Type v} →
    {E : ι → Type wE} →
      {E₁ : ι → Type wE₁} →
        {G : Type wG} →
          [inst : NontriviallyNormedField 𝕜] →
            [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)] →
              [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)] →
                [inst_3 : (i : ι) → SeminormedAddCommGroup (E₁ i)] →
                  [inst_4 : (i : ι) → NormedSpace 𝕜 (E₁ i)] →
                    [inst_5 : SeminormedAddCommGroup G] →
                      [inst_6 : NormedSpace 𝕜 G] →
                        [Fintype ι] →
                          [DecidableEq ι] →
                            ContinuousMultilinearMap 𝕜 E₁ G →
                              ((i : ι) → E i →L[𝕜] E₁ i) →
                                ((i : ι) → E i →L[𝕜] E₁ i) →L[𝕜] ContinuousMultilinearMap 𝕜 E G

Fréchet derivative of compContinuousLinearMap f g with respect to g. The derivative with respect to f is given by compContinuousLinearMapL.

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Basic

Cited by

9 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceFintypeDecidableEq