Theorems · Theorem · complex analysis

FormalMultilinearSeries.norm_compContinuousLinearMap_le

∀ {𝕜 : Type u_1} {E : Type u_3} {F : Type u_4} {G : Type u_5} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] (p : FormalMultilinearSeries 𝕜 F G) (u : E →L[𝕜] F)
  (n : ℕ), ‖p.compContinuousLinearMap u n‖ ≤ ‖p n‖ * ‖u‖ ^ n

Defined in

Mathlib.Analysis.Analytic.ConvergenceRadius

Cited by

2 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace