Theorems · Definition · functional analysis

PiTensorProduct.mapLMultilinear

{ι : Type u_1} →
  [inst : Fintype ι] →
    (𝕜 : Type u_2) →
      (E : ι → Type u_3) →
        [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)] →
          [inst_2 : NontriviallyNormedField 𝕜] →
            [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)] →
              (E' : ι → Type u_5) →
                [inst_4 : (i : ι) → SeminormedAddCommGroup (E' i)] →
                  [inst_5 : (i : ι) → NormedSpace 𝕜 (E' i)] →
                    ContinuousMultilinearMap 𝕜 (fun i => E i →L[𝕜] E' i)
                      ((PiTensorProduct 𝕜 fun i => E i) →L[𝕜] PiTensorProduct 𝕜 fun i => E' i)

The tensor of a family of linear maps from Eᵢ to E'ᵢ, as a continuous multilinear map of the family.

Defined in

Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm

Cited by

2 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceSeminormedAddCommGroupNormedSpace