On this MSE page, an answer mentions a cornucopia of vaguely similar results to Hurwitz's Theorem and Frobenius' Theorem, all of which say something like "Every XYZ division algebra is isomorphic to something in this small neat set." often consisting of an initial segment of $\mathbb{R}\subset \mathbb{C}\subset\mathbb{H}\subset\mathbb{H}$.
However, the answer mentions a "Gelfand Theorem" from 1939 which says "the commutative Banach division algebras are $\mathbb{R},\mathbb{C}$". Presumably this isn't true as is - do we have to assume they are real algebras? Even then, I can find no mention of this online or on Wikipedia etc. when it feels like it would be an incredibly important result to mention...
Does anyone know what this result actually said and can find a reference for it?