Reflexive cones

被引：5

作者：

Casini, E. ^{[1
]}

Miglierina, E. ^{[2
]}

Polyrakis, I. A. ^{[3
]}

Xanthos, F. ^{[3
]}

机构：

[1] Univ Insubria, Dipartimento Sci & Alta Tecnol, I-22100 Como, Italy

[2] Univ Cattolica Sacro Cuore, Dipartimento Discipline Matemat Finanza Matemat &, I-20123 Milan, Italy

[3] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

来源：

POSITIVITY | 2013年 / 17卷 / 03期

关键词：

Cones; Base for a cone; Vector lattices; Ordered Banach spaces; Geometry of cones; Weakly compact sets; Reflexivity; Positive Schauder bases;

D O I：

10.1007/s11117-012-0212-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Reflexive cones in Banach spaces are cones with weakly compact intersection with the unit ball. In this paper we study the structure of this class of cones. We investigate the relations between the notion of reflexive cones and the properties of their bases. This allows us to prove a characterization of reflexive cones in term of the absence of a subcone isomorphic to the positive cone of . Moreover, the properties of some specific classes of reflexive cones are investigated. Namely, we consider the reflexive cones such that the intersection with the unit ball is norm compact, those generated by a Schauder basis and the reflexive cones regarded as ordering cones in Banach spaces. Finally, it is worth to point out that a characterization of reflexive spaces and also of the spaces with the Schur property by the properties of reflexive cones is given.

引用

页码：911 / 933

页数：23

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