Theorems · Theorem · functional analysis

PiTensorProduct.dualSeminorms_bounded

Deprecated since 2026-06-10Mathlib marks this declaration as deprecated.

∀ {ι : Type uι} [inst : Fintype ι] {𝕜 : Type u𝕜} [inst_1 : NontriviallyNormedField 𝕜] {E : ι → Type uE}
  [inst_2 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)],
  BddAbove
    {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

2 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeNontriviallyNormedFieldSeminormedAddCommGroupNormedSpace