Theorems · Theorem · functional analysis

PiTensorProduct.liftEquiv_apply

∀ {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)] (F : Type u_4)
  [inst_4 : SeminormedAddCommGroup F] [inst_5 : NormedSpace 𝕜 F] (f : ContinuousMultilinearMap 𝕜 E F),
  (PiTensorProduct.liftEquiv 𝕜 E F) f = (PiTensorProduct.lift f.toMultilinearMap).mkContinuous ‖f‖ ⋯

Defined in

Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceSeminormedAddCommGroupNormedSpace