Theorems · Theorem · functional analysis

InnerProductSpace.adjoint_rankOne

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace 𝕜 E] [inst_4 : InnerProductSpace 𝕜 F]
  [inst_5 : CompleteSpace E] [inst_6 : CompleteSpace F] (x : E) (y : F),
  ContinuousLinearMap.adjoint (((InnerProductSpace.rankOne 𝕜) x) y) = ((InnerProductSpace.rankOne 𝕜) y) x

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

0 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedAddCommGroupInnerProductSpaceInnerProductSpaceCompleteSpaceCompleteSpace