I. Gelfand, M. Neumark (1943), Matematicheskii Sbornik 12(54):2, 197–217 (1943); reprinted in Contemporary Mathematics 167 (1994), 403–419 — DOI-10.1090/conm/167/16
Standing in the record
Registered on 2026-09-29 at the owner’s request, because the owner’s prior-art novelty map (a private working
document on concepts as projectors, the linear representation hypothesis and their neighbours) cites it: §2 item 2: the Gelfand leg of the Gelfand/Stone/Pontryagin duality tripod (operator face ↔ spectrum).
It is seeded from metadata and published descriptions and has not been read here.
Only the year of first publication is known; published: uses 1 January.
The map names this reference only loosely; this entry is one reasonable reading of it, and the choice is the owner’s to revise.
Identification notes: Map names only “Gelfand”. Chosen Gelfand–Naimark 1943 (contains the commutative C(X) theorem and the GNS-based embedding). Alternative: Gelfand 1941 “Normierte Ringe”, Mat. Sb. 9(51):3–24 (commutative Gelfand transform) — not registered. DOI is the 1994 AMS reprint (Crossref-verified); original on mathnet.ru (sm6155) could not be verified (HTTP 403 from here). Nucleation already holds GNS construction (Wikipedia), LIT-241 — related, not this paper.
It was filed Deferred, unread. NOTE-303 is the close reading of 2026-09-29, and it placed the work: Active — worth reading as the primary source of both Gelfand–Naimark theorems, commutative (Lemma 1) and non-commutative (Theorem 1), and of the GNS construction in embryo. It is compact and readable. Modern treatments state it with the single C*-identity. The authors themselves note that it suffices, and later work showed their extra axioms 5′ and 6′ redundant (not verified here).