Compact spaces associated to separable Banach lattices

被引：0

作者：

Aviles, Antonio ^{[1
]}

Martinez-Cervantes, Gonzalo ^{[2
]}

Rueda Zoca, Abraham ^{[1
]}

Tradacete, Pedro ^{[3
]}

机构：

[1] Univ Murcia, Dept Matemat, Campus Espinardo, Murcia 30100, Spain

[2] Univ Alicante, Fac Ciencias, Dept Matemat, Alicante 03080, Spain

[3] CSIC, Inst Ciencias Matemat CSIC UAM UC3M UCM, C Nicolas Cabrera,13-15,Campus Cantoblanco UAM, Madrid 28049, Spain

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2022年 / 16卷 / 04期

关键词：

Banach lattice; Structure space; IDEALS; REPRESENTATIONS;

D O I：

10.1007/s43037-022-00221-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 beta N. Some natural questions about this class are left open.

引用

页数：19

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