Theorems · Theorem · functional analysis

ContinuousLinearMap.lTensor_apply

∀ {𝕜 : Type u_1} {E : Type u_2} {G : Type u_4} {H : Type u_5} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : NormedAddCommGroup G] [inst_4 : InnerProductSpace 𝕜 G]
  [inst_5 : NormedAddCommGroup H] [inst_6 : InnerProductSpace 𝕜 H] (g : G →L[𝕜] H) (x : TensorProduct 𝕜 E G),
  (ContinuousLinearMap.lTensor E g) x = (LinearMap.lTensor E ↑g) x

Defined in

Mathlib.Analysis.InnerProductSpace.TensorProduct

Cited by

13 results in Mathlib

Foundations

Depth 264 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace