Cone characterization of Grothendieck spaces and Banach spaces containing c 0

Cone characterization of Grothendieck spaces and Banach spaces containing c 0 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 ℓ 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. Positivity Springer Journals

Cone characterization of Grothendieck spaces and Banach spaces containing c 0

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SP Birkhäuser Verlag Basel
Copyright © 2010 by Springer Basel AG
Mathematics; Potential Theory; Operator Theory; Fourier Analysis; Econometrics; Calculus of Variations and Optimal Control; Optimization
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