论文标题
c（x）的订单对真实空间
The order bidual of C(X) for a realcompact space
论文作者
论文摘要
众所周知，与Arens产品一起提供的紧凑型空间$ x $的$ \ Mathrm C（x）$的双重性是同构的，作为Banach代数为$ \ Mathrm c（\ tilde X）$，用于某些紧凑型Space $ \ tilde x $。空间$ \ tilde x $是同构的独特之处。我们为RealCompact空间建立了类似的结果：$ \ mathrm c（x）$的订单双重订单$ x $，当用Arens产品提供时，作为$ f $ -Algebra to $ f $ -algebra to $ \ mathrm c（\ tilde x）的$ f $ -algebra c（\ tilde x）$。空间$ \ tilde x $是同构的独特之处。
It is well known that the bidual of $\mathrm C(X)$ for a compact space $X$, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to $\mathrm C(\tilde X)$ for some compact space $\tilde X$. The space $\tilde X$ is unique up to homeomorphism. We establish a similar result for realcompact spaces: The order bidual of $\mathrm C(X)$ for a realcompact space $X$, when supplied with the Arens product, is isomorphic as an $f$-algebra to $\mathrm C(\tilde X)$ for some realcompact space $\tilde X$. The space $\tilde X$ is unique up to homeomorphism.
