Theorems · Theorem · functional analysis

ContinuousMultilinearMap.opNorm_add_le

∀ {𝕜 : Type u} {ι : Type v} {E : ι → Type wE} {G : Type wG} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)]
  [inst_3 : SeminormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G] [inst_5 : Fintype ι]
  (f g : ContinuousMultilinearMap 𝕜 E G), ‖f + g‖ ≤ ‖f‖ + ‖g‖

The operator norm satisfies the triangle inequality.

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Basic

Cited by

0 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceFintype