Theorems · Theorem · functional analysis

LinearIsometry.adjoint_comp_self

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_5} {E' : Type u_6} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : CompleteSpace E] [inst_4 : NormedAddCommGroup E']
  [inst_5 : InnerProductSpace 𝕜 E'] [inst_6 : CompleteSpace E'] (f : E →ₗᵢ[𝕜] E'),
  ContinuousLinearMap.adjoint f.toContinuousLinearMap ∘SL f.toContinuousLinearMap = 1

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

2 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace