On finite elements in vector lattices and Banach lattices

被引：9

作者：

Chen, ZL

Weber, MR ^{[1
]}

机构：

[1] Tech Univ Dresden, Fachrichtung Math, D-01062 Dresden, Germany

[2] SW Jiaotong Univ, Dept Math, Chengdu 610031, Peoples R China

来源：

MATHEMATISCHE NACHRICHTEN | 2006年 / 279卷 / 5-6期

关键词：

vector lattice; Banach lattice; finite element; order continuous norm;

D O I：

10.1002/mana.200410374

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In Archimedean vector lattices we show that each element of the band generated by a finite element is also finite. In vector lattices with the (PPP) and in Banach lattices we obtain some characterizations of finite elements by using the generalized order units for principal bands. In the case of Banach lattices with order continuous norm the ideal of all finite elements coincides with the linear span of all atoms. Some other related results and applications are included. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：495 / 501

页数：7

共 13 条

[1]

Aliprantis C. D., 1985, POSITIVE OPERATORS

[2] Relative weak compactness of solid hulls in Banach lattices [J].