Theorems · Theorem · functional analysis

LinearIsometryEquiv.conjStarAlgEquiv_apply_apply

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {H : Type u_5} [inst_1 : NormedAddCommGroup H] [inst_2 : InnerProductSpace 𝕜 H]
  [inst_3 : CompleteSpace H] {K : Type u_6} [inst_4 : NormedAddCommGroup K] [inst_5 : InnerProductSpace 𝕜 K]
  [inst_6 : CompleteSpace K] (e : H ≃ₗᵢ[𝕜] K) (x : H →L[𝕜] H) (y : K), (e.conjStarAlgEquiv x) y = e (x (e.symm y))

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

0 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace