Theorems · Theorem · functional analysis

lp.norm_dualPairing

∀ {ι : Type u_1} {𝕜 : Type u_2} {E : ι → Type u_3} {F : ι → Type u_4} [inst : RCLike 𝕜]
  [inst_1 : (i : ι) → NormedAddCommGroup (E i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)]
  [inst_3 : (i : ι) → NormedAddCommGroup (F i)] [inst_4 : (i : ι) → NormedSpace 𝕜 (F i)] {p q : ENNReal} {H : Type u_6}
  [inst_5 : NormedAddCommGroup H] [inst_6 : NormedSpace 𝕜 H] [inst_7 : CompleteSpace H] [inst_8 : Fact (1 ≤ p)]
  [inst_9 : Fact (1 ≤ q)] [inst_10 : p.HolderConjugate q] (B : (i : ι) → E i →L[𝕜] F i →L[𝕜] H) {K : NNReal}
  (hBK : ∀ (i : ι), ‖B i‖ ≤ ↑K), ‖lp.dualPairing p q B hBK‖ ≤ ↑K

Defined in

Mathlib.Analysis.Normed.Lp.lpHolder

Cited by

0 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceFactFactENNReal.HolderConjugate