论文标题
关于$ c_0 $ in Spaces $ c（k \ times l）$的可补充性
On complementability of $c_0$ in spaces $C(K\times L)$
论文作者
论文摘要
Using elementary probabilistic methods, in particular a variant of the Weak Law of Large Numbers related to the Bernoulli distribution, we prove that for every infinite compact spaces $K$ and $L$ the product $K\times L$ admits a sequence $\langleμ_n\colon n\in\mathbb{N}\rangle$ of normalized signed measures with finite supports which converges to $0$关于双Banach空间$ C（K \ Times L）^* $的弱*拓扑。我们的方法是完全建设性的 - 尺寸$μ_n$由明确的简单公式定义。我们还表明，此结果概括了cembranos和freniche的经典定理，该定理指出，对于每个无限的紧凑型空间$ k $和$ l $ banach space $ c（k \ times l）$包含space $ c_0 $的补充副本。
Using elementary probabilistic methods, in particular a variant of the Weak Law of Large Numbers related to the Bernoulli distribution, we prove that for every infinite compact spaces $K$ and $L$ the product $K\times L$ admits a sequence $\langleμ_n\colon n\in\mathbb{N}\rangle$ of normalized signed measures with finite supports which converges to $0$ with respect to the weak* topology of the dual Banach space $C(K\times L)^*$. Our approach is completely constructive -- the measures $μ_n$ are defined by an explicit simple formula. We also show that this result generalizes the classical theorem of Cembranos and Freniche which states that for every infinite compact spaces $K$ and $L$ the Banach space $C(K\times L)$ contains a complemented copy of the space $c_0$.
