论文标题
与可分开的Banach Lattices相关的紧凑空间
Compact spaces associated to separable Banach lattices
论文作者
论文摘要
我们研究了作为可分离Banach晶格的结构空间的紧凑空间。换句话说，我们分析了$ c（k）$的空间作为可分离的Banach Lattices的主要理想。除其他事项外，还表明，每个这样的compactum $ k $都承认了一个严格的阳性常规鲍尔（Analization Type），并且在不可渗透的情况下，这些compacta饱满了$β\ mathbb n $的副本。有关此课程的一些自然问题是开放的。
We study the class of compact spaces that appear as structure spaces of separable Banach lattices. In other words, we analyze what $C(K)$ spaces appear as principal ideals of separable Banach lattices. Among other things, it is shown that every such compactum $K$ admits a strictly positive regular Borel measure of countable type that is analytic, and in the nonmetrizable case these compacta are saturated with copies of $β\mathbb N$. Some natural questions about this class are left open.
