Theorems · Definition · functional analysis

StrongDual.extendRCLikeL

{𝕜 : Type u_4} →
  {F : Type u_5} →
    [inst : RCLike 𝕜] →
      [inst_1 : TopologicalSpace F] →
        [inst_2 : AddCommGroup F] →
          [inst_3 : Module 𝕜 F] →
            [ContinuousSMul 𝕜 F] → [inst_5 : Module ℝ F] → [IsScalarTower ℝ 𝕜 F] → StrongDual ℝ F ≃L[ℝ] StrongDual 𝕜 F

The extension StrongDual.extendRCLike as a continuous linear equivalence between the strong duals when scalar multiplication (by 𝕜) is jointly continuous.

Defined in

Mathlib.Analysis.Normed.Module.RCLike.Extend

Cited by

4 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeTopologicalSpaceAddCommGroupModuleContinuousSMulModuleIsScalarTower