Theorems · Definition · operator theory

LinearPMap.adjointDomainMkCLM

{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] → (T : E →ₗ.[𝕜] F) → ↥T.adjointDomain → StrongDual 𝕜 ↥T.domain

The operator fun x ↦ ⟪y, T x⟫ considered as a continuous linear operator from T.adjointDomain to 𝕜.

Defined in

Mathlib.Analysis.InnerProductSpace.LinearPMap

Cited by

2 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace