Theorems · Theorem · functional analysis

StrongDual.norm_extendRCLike_bound

∀ {𝕜 : Type u_1} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup F] [inst_2 : NormedSpace 𝕜 F]
  [inst_3 : NormedSpace ℝ F] [inst_4 : IsScalarTower ℝ 𝕜 F] (fr : StrongDual ℝ F) (x : F),
  ‖fr.extendRCLike x‖ ≤ ‖fr‖ * ‖x‖

The norm of the extension is bounded by ‖fr‖.

Defined in

Mathlib.Analysis.Normed.Module.RCLike.Extend

Cited by

2 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupNormedSpaceNormedSpaceIsScalarTower