Theorems · Theorem · operator theory

LinearMap.IsSymmetric.continuous

• 1000+ list: Hellinger–Toeplitz theorem

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  [CompleteSpace E] {T : E →ₗ[𝕜] E}, T.IsSymmetric → Continuous ⇑T

The Hellinger--Toeplitz theorem: if a symmetric operator is defined on a complete space, then it is automatically continuous.

Defined in

Mathlib.Analysis.InnerProductSpace.Symmetric

Cited by

0 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace