Theorems · Definition · functional analysis

ContinuousLinearMap.flipAlternating

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

Flip arguments in f : F →L[𝕜] E [⋀^ι]→L[𝕜] G to get ⋀^ι⟮𝕜; E; F →L[𝕜] G⟯

Defined in

Mathlib.Analysis.Normed.Module.Alternating.Basic

Cited by

6 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceFintype