On the geometry of proportional quotients of ${l^m_1}$

Volume 155 / 2003

Piotr Mankiewicz, Stanisław J. Szarek Studia Mathematica 155 (2003), 51-66 MSC: 46B07, 46B09, 46B20. DOI: 10.4064/sm155-1-4


We compare various constructions of random proportional quotients of $l_1^m$ (i.e., with the dimension of the quotient roughly equal to a fixed proportion of $m$ as $m \rightarrow \infty $) and show that several of those constructions are equivalent. As a consequence of our approach we conclude that the most natural “geometric” models possess a number of asymptotically extremal properties, some of which were hitherto not known for any model.


  • Piotr MankiewiczInstitute of Mathematics
    Polish Academy of Sciences
    /Sniadeckich 8
    00-950 Warszawa, Poland
  • Stanisław J. SzarekÉquipe d'Analyse Fonctionnelle
    Université Paris VI, B.C. 186
    4, Place Jussieu
    75252 Paris, France

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