Abstract of a paper by S. J. Dilworth, Denka Kutzarova, G. Lancien, and N. L. Randrianarivony Title: Asymptotic geometry of Banach spaces and uniform quotient maps
This is an announcement for the paper "Asymptotic geometry of Banach spaces and uniform quotient maps" by S. J. Dilworth, Denka Kutzarova, G. Lancien, and N. L. Randrianarivony. Abstract: 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. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B80 (Primary), 46B20 (Secondary) Submitted from: nrandria@slu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.0501 or http://arXiv.org/abs/1209.0501
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