Theorems · Theorem · operator theory

LinearPMap.IsFormalAdjoint.le_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] {T : E →ₗ.[𝕜] F}
  {S : F →ₗ.[𝕜] E} [inst_5 : CompleteSpace E], Dense ↑T.domain → T.IsFormalAdjoint S → S ≤ T.adjoint

The adjoint is maximal in the sense that it contains every formal adjoint.

Defined in

Mathlib.Analysis.InnerProductSpace.LinearPMap

Cited by

0 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace