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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2013

Asymptotic geometry of Banach spaces and non linear quotients.

Résumé

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.
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hal-00825066 , version 1 (22-05-2013)

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  • HAL Id : hal-00825066 , version 1

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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⟩
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