Theorems · Definition · functional analysis

ContinuousMultilinearMap.flipLinear

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

Flip arguments in f : ContinuousMultilinearMap 𝕜 E (G →L[𝕜] G') to get G →L[𝕜] ContinuousMultilinearMap 𝕜 E G'

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Basic

Cited by

5 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceFintype