Gelfand-Naimark theorem states that every commutative C-* algebra is isometric to $C(M)$, the ring of continuous functions over its spectrum. Is the theorem true for ordinary commutative Banach semisimple algebras, i.e. without *? Every proof that the Gelfand transform is an isometry uses the fact that in C-* algebra $|xx^{*}| = |x|^{2}$, so I wonder whether it is true when we don't have the * and that identity. If it is not isometric, is it isomorphic?(adsbygoogle = window.adsbygoogle || []).push({});

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# Question about Gelfand-Naimark

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