Theorems · Definition · functional analysis

Module.Dual.extendRCLike

{𝕜 : Type u_1} →
  [inst : RCLike 𝕜] →
    {F : Type u_2} →
      [inst_1 : AddCommGroup F] →
        [inst_2 : Module ℝ F] → [inst_3 : Module 𝕜 F] → [IsScalarTower ℝ 𝕜 F] → Module.Dual ℝ F → Module.Dual 𝕜 F

Extend fr : Dual ℝ F to Dual 𝕜 F in a way that will also be continuous and have its norm (as a continuous linear map) equal to ‖fr‖ when fr is itself continuous on a normed space.

Defined in

Mathlib.Analysis.RCLike.Extend

Cited by

12 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeAddCommGroupModuleModuleIsScalarTower