On the geometry of proportional quotients of $l₁^{m}$

• Autorzy: Piotr Mankiewicz , Stanisław J. Szarek
• Języki publikacji: EN

Abstrakty

EN

We compare various constructions of random proportional quotients of $l₁^{m}$ (i.e., with the dimension of the quotient roughly equal to a fixed proportion of m as m → ∞) 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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B07: Local theory of Banach spaces
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 1
• Strony: 51-66

Daty

wydano

2003

Twórcy

autor

Piotr Mankiewicz

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

autor

Stanisław J. Szarek

• Équipe d'Analyse Fonctionnelle, Université Paris VI, B.C. 186, 4, Place Jussieu, 75252 Paris, France

Identyfikatory

DOI

10.4064/sm155-1-4