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arXiv · 1209.0501

Asymptotic geometry of Banach spaces and uniform quotient maps

S. J. Dilworth·Denka Kutzarova·G. Lancien·N. L. Randrianarivony
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Abstract

Recently, Lima and Randrianarivony pointed out the role of the property $(β)$ 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 $(β)$ of the domain space. We also provide conditions under which this comparison can be improved.

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S. J. Dilworth, Denka Kutzarova, G. Lancien, N. L. Randrianarivony. 2012-09-03. Asymptotic geometry of Banach spaces and uniform quotient maps. https://arxiv.org/abs/1209.0501

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