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