Theorems · Theorem · functional analysis

PiTensorProduct.injectiveSeminorm_def

∀ {ι : Type u_2} [inst : Fintype ι] {𝕜 : Type u_3} [inst_1 : NontriviallyNormedField 𝕜] {E : ι → Type u_4}
  [inst_2 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)],
  PiTensorProduct.injectiveSeminorm =
    sSup
      {p |
        ∃ G x x_1,
          p =
            (normSeminorm 𝕜 (ContinuousMultilinearMap 𝕜 E G →L[𝕜] G)).comp
              (PiTensorProduct.toDualContinuousMultilinearMap G)}

Defined in

Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm

Cited by

3 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeNontriviallyNormedFieldSeminormedAddCommGroupNormedSpace