Theorems · Definition · functional analysis

ContinuousLinearMapWOT.algEquiv

{𝕜₁ : Type u_1} →
  [inst : NormedField 𝕜₁] →
    {E : Type u_3} →
      [inst_1 : AddCommGroup E] →
        [inst_2 : TopologicalSpace E] →
          [inst_3 : Module 𝕜₁ E] →
            (S : Type u_5) →
              [inst_4 : CommSemiring S] →
                [inst_5 : Module S E] →
                  [inst_6 : SMulCommClass 𝕜₁ S E] →
                    [inst_7 : SMul S 𝕜₁] →
                      [inst_8 : IsScalarTower S 𝕜₁ E] →
                        [inst_9 : ContinuousConstSMul S E] →
                          [inst_10 : IsTopologicalAddGroup E] → (E →WOT[𝕜₁] E) ≃ₐ[S] E →L[𝕜₁] E

The algebra equivalence between ContinuousLinearMapWOT and ContinuousLinearMap.

Defined in

Mathlib.Analysis.LocallyConvex.WeakOperatorTopology

Cited by

2 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupTopologicalSpaceModuleCommSemiringModuleSMulCommClassSMulIsScalarTowerContinuousConstSMulIsTopologicalAddGroup