Theorems · Theorem · functional analysis

PiTensorProduct.opNorm_mapL

∀ {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)] {E' : ι → Type u_5}
  [inst_4 : (i : ι) → SeminormedAddCommGroup (E' i)] [inst_5 : (i : ι) → NormedSpace 𝕜 (E' i)]
  (f : (i : ι) → E i →L[𝕜] E' i), ‖PiTensorProduct.mapL f‖ ≤ ∏ i, ‖f i‖

Defined in

Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm

Cited by

0 results in Mathlib

Foundations

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

Assumes

FintypeSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceSeminormedAddCommGroupNormedSpace