Theorems · Definition · operator theory

LinearPMap.adjoint

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : RCLike 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : InnerProductSpace 𝕜 E] →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : InnerProductSpace 𝕜 F] → (E →ₗ.[𝕜] F) → [CompleteSpace E] → F →ₗ.[𝕜] E

The adjoint operator as a partially defined linear operator, denoted as T†.

Defined in

Mathlib.Analysis.InnerProductSpace.LinearPMap

Cited by

13 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace