Theorems · Definition · functional analysis

ContinuousLinearMap.adjoint

{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] → [CompleteSpace E] → [CompleteSpace F] → (E →L[𝕜] F) ≃ₗᵢ⋆[𝕜] F →L[𝕜] E

The adjoint of a bounded operator A from a Hilbert space E to another Hilbert space F, denoted as A†.

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

82 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedAddCommGroupInnerProductSpaceInnerProductSpaceCompleteSpaceCompleteSpace