Cones with bounded and unbounded bases and reflexivity

Enrico Miglierina, E. Casini, E. Miglierina

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

13 Citazioni (Scopus)


In this paper we prove two characterizations of reflexivity for a Banach space X. The first one is based on the existence in X of a closed convex cone with nonempty interior such that all the bases generated by a strictly positive functional are bounded, while the second one is stated in terms of non existence of a cone such that has bounded and unbounded bases (both generated by strictly positive functionals) simultaneously. We call such a cone mixed based cone. We study the features of this class of cones. In particular, we show that every cone conically isomorphic to the nonnegative orthant ℓ^1 of ℓ^1 is a mixed based cone and that every mixed based cone contains a conically isomorphic copy of ℓ^1_+. Moreover we give a detailed description of the structure of a mixed based cone. This approach allows us to prove some results concerning the embeddings of ℓ^1 and c_0 in a Banach space.
Lingua originaleEnglish
pagine (da-a)2356-2366
Numero di pagine11
Stato di pubblicazionePubblicato - 2010


  • Based cone
  • Cone conically isomorphic to l^1_+
  • Reflexive space
  • Strongly summing sequence


Entra nei temi di ricerca di 'Cones with bounded and unbounded bases and reflexivity'. Insieme formano una fingerprint unica.

Cita questo