Theorems · Definition · functional analysis

PiTensorProduct.mapLMonoidHom

{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)] →
              ((i : ι) → E i →L[𝕜] E i) →* (PiTensorProduct 𝕜 fun i => E i) →L[𝕜] PiTensorProduct 𝕜 fun i => E i

Upgrading PiTensorProduct.mapL to a MonoidHom when E = E'.

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

FintypeSeminormedAddCommGroupNontriviallyNormedFieldNormedSpace