Asymptotic geometry of Banach spaces and non linear quotients.

Stephen Dilworth (1) , Denka Kutzarova (2) , Gilles Lancien (3) , Lovasoa Randrianarivony (4)

1 Department of Mathematics [Columbia]
2 Institute of Mathematics, Bulgarian Academy of Sciences.
3 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
4 Department of Mathematics and Computer Science, Saint Louis University.

Recently, Lima and Randrianarivony pointed out the role of the property (beta ) of Rolewicz in nonlinear quotient problems, and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of (beta ) of the domain space. We also provide conditions under which this comparison can be improved.

Domaines: Analyse fonctionnelle [math.FA]

Stephen Dilworth, Denka Kutzarova, Gilles Lancien, Lovasoa Randrianarivony. Asymptotic geometry of Banach spaces and non linear quotients.. Proceedings of the American Mathematical Society, 2013. ⟨hal-00825066⟩