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Positivity

, Volume 15, Issue 4, pp 677–693 | Cite as

Cone characterization of Grothendieck spaces and Banach spaces containing c 0

  • Ioannis A. PolyrakisEmail author
  • Foivos Xanthos
Article

Abstract

In this article we study the embeddability of cones in a Banach space X. First we prove that c 0 is embeddable in X if and only if its positive cone \({c_0^+}\) is embeddable in X and we study some properties of Banach spaces containing c 0 in the light of this result. So, unlike with the positive cone of 1 which is embeddable in any non-reflexive space, \({c_0^+}\) has the same behavior as the whole space c 0. In the second part of this article we give a characterization of Grothendieck spaces X according to the geometry of cones of X*. By these results we give a partial positive answer to a problem of J.H. Qiu concerning the geometry of cones.

Keywords

Cones Bases for cones Conic isomorphisms Grothendieck spaces \({c_0^+}\) \({\ell_1^+}\) 

Mathematics Subject Classification (2000)

46B03 46B40 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece

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