Theorems · Definition · functional analysis

ContinuousLinearEquiv.conjContinuousAlgEquiv

{𝕜 : Type u_1} →
  {G : Type u_4} →
    {H : Type u_5} →
      [inst : AddCommGroup G] →
        [inst_1 : AddCommGroup H] →
          [inst_2 : NormedField 𝕜] →
            [inst_3 : Module 𝕜 G] →
              [inst_4 : Module 𝕜 H] →
                [inst_5 : TopologicalSpace G] →
                  [inst_6 : TopologicalSpace H] →
                    [inst_7 : IsTopologicalAddGroup G] →
                      [inst_8 : IsTopologicalAddGroup H] →
                        [inst_9 : ContinuousConstSMul 𝕜 G] →
                          [inst_10 : ContinuousConstSMul 𝕜 H] → (G ≃L[𝕜] H) → (G →L[𝕜] G) ≃A[𝕜] H →L[𝕜] H

A continuous linear equivalence of two spaces induces a continuous equivalence of algebras of their endomorphisms.

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

10 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupNormedFieldModuleModuleTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroupContinuousConstSMulContinuousConstSMul