Theorems · Theorem · operator theory

LinearPMap.mem_adjoint_domain_of_exists

∀ {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}
  [inst_5 : CompleteSpace E] (y : F), (∃ w, ∀ (x : ↥T.domain), inner 𝕜 w ↑x = inner 𝕜 y (↑T x)) → y ∈ T.adjoint.domain

Defined in

Mathlib.Analysis.InnerProductSpace.LinearPMap

Cited by

2 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace