Let $C(K)$ be the Banach algebra of real-valued continuous functions on a compact Hausdorff space $K$. It is known that the bidual of $C(K)$ is again a $C(\Omega)$ space, for some compact Hausdorff space $\Omega$. Is $C(K)$ a subalgebra in its bidual? If the answer is in the positive, is $C(K)$ embedded in its bidual as a subalgebra via the canonical isometric embedding, that is, $f \mapsto \int_{K} f d\mu$, for each $\mu \in C(K)^{\ast}$?
2026-03-27 19:32:15.1774639935
Is C(K) a subalgebra in its bidual?
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