On the geometry of proportional quotients of ${l^m_1}$
Volume 155 / 2003
Studia Mathematica 155 (2003), 51-66
MSC: 46B07, 46B09, 46B20.
DOI: 10.4064/sm155-1-4
Abstract
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.
