DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The canonical evaluation map into the bidual

Definition

Let $K = R$ or $C$ . For a normed $X$ , define $J_{X} : X \to X^{* *}, (J_{X} x) (f) = f (x) (f \in X^{*}) .$ With the dual norm from The dual space X^* of a normed space and its dual norm, evaluation is linear in $f$ and $∣ (J_{X} x) (f) ∣ \leq ∥ x ∥ ∥ f ∥$ , so $J_{X} x$ is a bounded functional on $X^{*}$ . The map is canonical and uses no chosen basis or conjugation.

The canonical evaluation map into the bidual

Definition

Depends on

Dependency tree · 2 levels

Sources