Theorems · Theorem · functional analysis

ContinuousLinearMapWOT.ext_inner_iff

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : AddCommGroup E] [inst_2 : TopologicalSpace E]
  [inst_3 : Module 𝕜 E] [inst_4 : NormedAddCommGroup F] [inst_5 : InnerProductSpace 𝕜 F] {A B : E →WOT[𝕜] F},
  A = B ↔ ∀ (x : E) (y : F), inner 𝕜 y (A x) = inner 𝕜 y (B x)

Defined in

Mathlib.Analysis.InnerProductSpace.WeakOperatorTopology

Cited by

0 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeAddCommGroupTopologicalSpaceModuleNormedAddCommGroupInnerProductSpace