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

Tom 155 / 2003

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

Streszczenie

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.

Autorzy

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

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