Theorems · Theorem · functional analysis

TensorProduct.mapL_comp

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} {H : Type u_5} [inst : RCLike 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : NormedAddCommGroup F]
  [inst_4 : InnerProductSpace 𝕜 F] [inst_5 : NormedAddCommGroup G] [inst_6 : InnerProductSpace 𝕜 G]
  [inst_7 : NormedAddCommGroup H] [inst_8 : InnerProductSpace 𝕜 H] {A : Type u_6} {B : Type u_7}
  [inst_9 : NormedAddCommGroup A] [inst_10 : InnerProductSpace 𝕜 A] [inst_11 : NormedAddCommGroup B]
  [inst_12 : InnerProductSpace 𝕜 B] (f₁ : E →L[𝕜] F) (f₂ : A →L[𝕜] E) (g₁ : G →L[𝕜] H) (g₂ : B →L[𝕜] G),
  TensorProduct.mapL (f₁ ∘SL f₂) (g₁ ∘SL g₂) = TensorProduct.mapL f₁ g₁ ∘SL TensorProduct.mapL f₂ g₂

Defined in

Mathlib.Analysis.InnerProductSpace.TensorProduct

Cited by

1 results in Mathlib

Foundations

Depth 266 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace