Theorems · Theorem · functional analysis

ContinuousMultilinearMap.compContinuousLinearMapL_apply

∀ {𝕜 : Type u_1} {ι : Type u_2} {E : ι → Type u_3} {F : Type u_4} [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 : AddCommGroup F] [inst_5 : Module 𝕜 F] [inst_6 : TopologicalSpace F]
  [inst_7 : IsTopologicalAddGroup F] {E₁ : ι → Type u_5} [inst_8 : (i : ι) → TopologicalSpace (E₁ i)]
  [inst_9 : ContinuousConstSMul 𝕜 F] [inst_10 : (i : ι) → AddCommGroup (E₁ i)] [inst_11 : (i : ι) → Module 𝕜 (E₁ i)]
  (f : (i : ι) → E i →L[𝕜] E₁ i) (g : ContinuousMultilinearMap 𝕜 E₁ F),
  (ContinuousMultilinearMap.compContinuousLinearMapL f) g = g.compContinuousLinearMap f

Defined in

Mathlib.Topology.Algebra.Module.Multilinear.Topology

Cited by

1 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldTopologicalSpaceAddCommGroupModuleAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupTopologicalSpaceContinuousConstSMulAddCommGroupModule