Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces K1, …, K n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each K i is scattered.

中文翻译：

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连续函数的 BANACH 空间的投影张量积的主观性

Galego 和 Samuel 表明，如果ķ, L是可度量的紧致豪斯多夫空间，则 $C(K)\widehat{\otimes}_\pi C(L)$ 是C0-饱和当且仅当它是次投影当且仅当ķ和大号都是分散的。我们从他们的结果中删除了可度量性的假设，并将其从双重投影张量积的情况扩展到一般n-fold 投影张量积以表明对于任何 $n\in\mathbb{N}$ 紧凑的豪斯多夫空间ķ1, …,ķ n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ 是C0-饱和当且仅当它是次投影当且仅当每个ķ 一世 是分散的。