Theorems · Theorem · functional analysis

ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_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 : ContinuousMultilinearMap 𝕜 E G) {m : (i : ι) → E i} {b : ℝ}, ‖m‖ ≤ b → ‖f m‖ ≤ ‖f‖ * b ^ Fintype.card ι

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceFintype