Theorems · Theorem · functional analysis

StrongDual.extendRCLike_apply

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {F : Type u_2} [inst_1 : TopologicalSpace F] [inst_2 : AddCommGroup F]
  [inst_3 : Module 𝕜 F] [inst_4 : ContinuousConstSMul 𝕜 F] [inst_5 : Module ℝ F] [inst_6 : IsScalarTower ℝ 𝕜 F]
  (fr : StrongDual ℝ F) (x : F), fr.extendRCLike x = ↑(fr x) - RCLike.I * ↑(fr (RCLike.I • x))

Defined in

Mathlib.Analysis.RCLike.Extend

Cited by

2 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeTopologicalSpaceAddCommGroupModuleContinuousConstSMulModuleIsScalarTower