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.

A closable densely defined linear operator

Definition

Let $X$ and $Y$ be normed spaces, and let $A : D (A) \subseteq X \to Y$ be linear with dense linear domain. It is closable when the closure of its graph (The graph of a linear operator with a linear domain) in $X \times Y$ (Interior, closure, boundary, limit point, isolated point and dense subset of a metric space) is itself the graph of a linear operator. That operator is the closure $\overline{A}$ .

Depends on

Used by

Dependency tree · two levels

8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Buhler--Salamon, Functional Analysis, Definition 2.25 (standard reference, not scraped)