Theorems · Theorem · functional analysis

ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply

∀ {𝕜 : Type u_1} {ι : Type u_2} {E : ι → Type u_3} {E₁ : ι → Type u_4} {F : Type u_5} [inst : NormedField 𝕜]
  [inst_1 : (i : ι) → TopologicalSpace (E i)] [inst_2 : (i : ι) → AddCommGroup (E i)]
  [inst_3 : (i : ι) → Module 𝕜 (E i)] [inst_4 : (i : ι) → TopologicalSpace (E₁ i)]
  [inst_5 : (i : ι) → AddCommGroup (E₁ i)] [inst_6 : (i : ι) → Module 𝕜 (E₁ i)] [inst_7 : AddCommGroup F]
  [inst_8 : Module 𝕜 F] [inst_9 : TopologicalSpace F] [inst_10 : IsTopologicalAddGroup F]
  [inst_11 : ContinuousConstSMul 𝕜 F] (g : ContinuousMultilinearMap 𝕜 E₁ F) (f : (i : ι) → E i ≃L[𝕜] E₁ i),
  (ContinuousLinearEquiv.continuousMultilinearMapCongrLeft F f) g = g.compContinuousLinearMap fun i => ↑(f i)

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Topology

Cited by

0 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldTopologicalSpaceAddCommGroupModuleTopologicalSpaceAddCommGroupModuleAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul