Theorems · Theorem · functional analysis

ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply

∀ {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] (e : G ≃L[𝕜] H) (f : G →L[𝕜] G) (x : H),
  (e.conjContinuousAlgEquiv f) x = e (f (e.symm x))

Defined in

Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap

Cited by

0 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupNormedFieldModuleModuleTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupIsTopologicalAddGroupContinuousConstSMulContinuousConstSMul