Theorems · Definition · operator theory

LinearPMap.adjointAux

{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} → [CompleteSpace E] → Dense ↑T.domain → ↥T.adjointDomain →ₗ[𝕜] E

The adjoint as a linear map from its domain to E. This is an auxiliary definition needed to define the adjoint operator as a LinearPMap without the assumption that T.domain is dense.

Defined in

Mathlib.Analysis.InnerProductSpace.LinearPMap

Cited by

6 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace