Abstract

Reflexive cones in Banach spaces are cones with weakly compact intersec- tion 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 ℓ1. 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 a Banach spaces. Finally, it is worth to point out that a characterization of reflexive spaces and also of the Schur spaces by the properties of reflexive cones is given.
Original languageEnglish
Number of pages23
Publication statusPublished - 2012

Keywords

  • Base for a cone
  • Cones
  • geometry of cones
  • ordered Banach spaces
  • positive Schauder bases
  • reflexivity
  • weakly compact sets

Fingerprint

Dive into the research topics of 'Reflexive cones'. Together they form a unique fingerprint.

Cite this