论文标题
连续功能Banach空间的投射张量产物的量子标记
Subprojectivity of projective tensor products of Banach spaces of continuous functions
论文作者
论文摘要
Galego和Samuel表明，如果$ k，l $是可以Metrizable，紧凑的，Hausdorff空间，则$ c（k）\ wideHat {\ otimes}_πc（l）$是$ c_0 $饱和的，并且仅当它是$ k $ g $和$ k $和$ l $均可分散的时，只有$ c_0 $饱和。我们从其结果中删除了衡量性的假设，并将其从两倍的投射张量产品扩展到一般的$ n $ fold射击量张量产品，以表明对于任何$ n \ in \ Mathbb {n} $ in \ Mathbb {n} $ and Compact and Compact and Compact and Compact and Compact，Hausdorff spaces $ k_1，\ ldots，\ ldots，k_n $，$ n $，$ \ \ \ \ \ \ \ wide， i = 1}^n c（k_i）$是$ c_0 $ - 饱和时，仅当它是subprojective时，并且仅当每个$ k_i $都散布时。
Galego and Samuel showed that if $K,L$ are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_πC(L)$ is $c_0$-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 two-fold projective tensor product to the general $n$-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces $K_1, \ldots, K_n$, $\widehat{\otimes}_{π, i=1}^n C(K_i)$ is $c_0$-saturated if and only if it is subprojective if and only if each $K_i$ is scattered.
