Geodesic
On the geometry of proportional quotients of ${l^m_1}$
Piotr Mankiewicz 1   ; Stanisław J. Szarek 2
1 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-950 Warszawa, Poland
2 Équipe d'Analyse Fonctionnelle Université Paris VI, B.C. 186 4, Place Jussieu 75252 Paris, France
Studia Mathematica, Tome 155 (2003) no. 1, pp. 51-66 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm155-1-4
Keywords: compare various constructions random proportional quotients dimension quotient roughly equal fixed proportion rightarrow infty several those constructions equivalent consequence approach conclude natural geometric models possess number asymptotically extremal properties which hitherto known model

Piotr Mankiewicz  1   ; Stanisław J. Szarek  2

1 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-950 Warszawa, Poland
2 Équipe d'Analyse Fonctionnelle Université Paris VI, B.C. 186 4, Place Jussieu 75252 Paris, France 
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Piotr Mankiewicz; Stanisław J. Szarek. On the geometry of proportional quotients of ${l^m_1}$. Studia Mathematica, Tome 155 (2003) no. 1, pp. 51-66. doi: 10.4064/sm155-1-4

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