Theorems · Theorem · functional analysis

ContinuousLinearMap.inner_map_map_of_mem_unitary

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {H : Type u_5} [inst_1 : NormedAddCommGroup H] [inst_2 : InnerProductSpace 𝕜 H]
  [inst_3 : CompleteSpace H] {u : H →L[𝕜] H}, u ∈ unitary (H →L[𝕜] H) → ∀ (x y : H), inner 𝕜 (u x) (u y) = inner 𝕜 x y

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

1 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace