Theorems · Theorem · functional analysis

ContinuousLinearMapWOT.postcompCLM_apply

∀ {𝕜₁ : Type u_5} {𝕜₂ : Type u_6} {𝕜₃ : Type u_7} {E : Type u_9} {F : Type u_10} {G : Type u_11} [inst : NormedField 𝕜₁]
  [inst_1 : NormedField 𝕜₂] [inst_2 : NormedField 𝕜₃] {σ₁₂ : 𝕜₁ →+* 𝕜₂} {σ₁₃ : 𝕜₁ →+* 𝕜₃} {σ₂₃ : 𝕜₂ →+* 𝕜₃}
  [inst_3 : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] [inst_4 : AddCommGroup E] [inst_5 : TopologicalSpace E]
  [inst_6 : Module 𝕜₁ E] [inst_7 : AddCommGroup F] [inst_8 : TopologicalSpace F] [inst_9 : Module 𝕜₂ F]
  [inst_10 : AddCommGroup G] [inst_11 : TopologicalSpace G] [inst_12 : Module 𝕜₃ G] [inst_13 : IsTopologicalAddGroup F]
  [inst_14 : ContinuousConstSMul 𝕜₂ F] [inst_15 : IsTopologicalAddGroup G] [inst_16 : ContinuousConstSMul 𝕜₃ G]
  [inst_17 : RingHomSurjective σ₂₃] [inst_18 : RingHomIsometric σ₂₃] (g : F →SWOT[σ₂₃] G) (f : E →SWOT[σ₁₂] F),
  g.postcompCLM f = g.comp f

Defined in

Mathlib.Analysis.LocallyConvex.WeakOperatorTopology

Cited by

0 results in Mathlib

Foundations

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

Assumes

NormedFieldNormedFieldNormedFieldRingHomCompTripleAddCommGroupTopologicalSpaceModuleAddCommGroupTopologicalSpaceModuleAddCommGroupTopologicalSpaceModuleIsTopologicalAddGroupContinuousConstSMulIsTopologicalAddGroupContinuousConstSMulRingHomSurjectiveRingHomIsometric