Mathematische Annalen

, Volume 367, Issue 3–4, pp 1777–1790 | Cite as

Shellable weakly compact subsets of C[0, 1]

  • J. Lopez-Abad
  • P. Tradacete


We show that for every weakly compact subset K of C[0, 1] with finite Cantor–Bendixson rank, there is a reflexive Banach lattice E and an operator \(T:E\rightarrow C[0,1]\) such that \(K\subseteq T(B_E)\). On the other hand, we exhibit an example of a weakly compact set of C[0, 1] homeomorphic to \(\omega ^\omega +1\) for which such T and E cannot exist. This answers a question of M. Talagrand in the 80’s.

Mathematics Subject Classification

46B50 46B42 47B07 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Instituto de Ciencias Matematicas (ICMAT)CSIC-UAM-UC3M-UCMMadridSpain
  2. 2.Mathematics DepartmentUniversidad Carlos III de MadridLeganés (Madrid)Spain

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