Theorems · Theorem · functional analysis

ContinuousLinearMap.adjoint_rTensor

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} (G : Type u_4) [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 : CompleteSpace E] [CompleteSpace G]
  [inst_9 : CompleteSpace (TensorProduct 𝕜 E G)] [inst_10 : CompleteSpace (TensorProduct 𝕜 F G)]
  [inst_11 : CompleteSpace F] (f : E →L[𝕜] F),
  ContinuousLinearMap.adjoint (ContinuousLinearMap.rTensor G f) =
    ContinuousLinearMap.rTensor G (ContinuousLinearMap.adjoint f)

Defined in

Mathlib.Analysis.InnerProductSpace.TensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceCompleteSpaceCompleteSpaceCompleteSpaceCompleteSpaceCompleteSpace