The free Banach lattice generated by a lattice

被引：5

作者：

Aviles, Antonio ^{[1
]}

Rodriguez Abellan, Jose David ^{[1
]}

机构：

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

来源：

POSITIVITY | 2019年 / 23卷 / 03期

关键词：

Free Banach lattice; Lattice; Linear order; Countable chain condition; 46B43; 06BXX;

D O I：

10.1007/s11117-018-0626-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the free Banach lattice generated by a lattice L. We give an explicit description of it and we study some of its properties for the case when L is a linear order, like the countable chain condition.

引用

页码：581 / 597

页数：17

共 8 条

[1] Chain conditions in free Banach lattices
Aviles, Antonio
Plebanek, Grzegorz
Rodriguez Abellan, Jose David
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 465 (02) : 1223 - 1229
[2] The free Banach lattice generated by a Banach space
Aviles, Antonio
Rodriguez, Jose
Tradacete, Pedro
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2018, 274 (10) : 2955 - 2977
[3] Birkhoff G., 1967, Lattice Theory, Vthird
[4] Free and projective Banach lattices
de Pagter, Ben
Wickstead, Anthony W.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2015, 145 (01) : 105 - 143
[5] Gratzer G, 1978, GEN LATTICE THEORY M
[6] Lindenstrauss J., 1979, Ergeb. Math. Grenzgeb., V97
[7] Schaefer HH., 1974, Banach Lattices and Positive Operators, DOI 10.1007/978-3-642-65970-6
[8] Todorcevic S., 1984, Handbook of Set-Theoretic Topology, P235

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