Theorems · Theorem · functional analysis

PiTensorProduct.mapL_id

∀ {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)],
  (PiTensorProduct.mapL fun i => ContinuousLinearMap.id 𝕜 (E i)) =
    ContinuousLinearMap.id 𝕜 (PiTensorProduct 𝕜 fun i => E i)

Defined in

Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm

Cited by

1 results in Mathlib

Foundations

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

Assumes

FintypeSeminormedAddCommGroupNontriviallyNormedFieldNormedSpace