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Asymptotic geometry of Banach spaces and uniform quotient maps


Authors: S. J. Dilworth, Denka Kutzarova, G. Lancien and N. L. Randrianarivony
Journal: Proc. Amer. Math. Soc. 142 (2014), 2747-2762
MSC (2010): Primary 46B80; Secondary 46B20
DOI: https://doi.org/10.1090/S0002-9939-2014-12001-6
Published electronically: April 25, 2014
MathSciNet review: 3209329
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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.


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Additional Information

S. J. Dilworth
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email: dilworth@math.sc.edu

Denka Kutzarova
Affiliation: Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Address at time of publication: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: denka@math.uiuc.edu

G. Lancien
Affiliation: Université de Franche-Comté, Laboratoire de Mathématiques UMR 6623, 16 route de Gray, 25030 Besançon Cedex, France
Email: gilles.lancien@univ-fcomte.fr

N. L. Randrianarivony
Affiliation: Department of Mathematics and Computer Science, St. Louis University, St. Louis, Missouri 63103
Email: nrandria@slu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12001-6
Received by editor(s): March 27, 2012
Received by editor(s) in revised form: August 24, 2012, and September 3, 2012
Published electronically: April 25, 2014
Additional Notes: The first author was partially supported by NSF grant DMS1101490
All authors were supported by the Workshop in Analysis and Probability at Texas A&M University in summer 2011
The fourth author was supported in part by a Young Investigator award from this NSF funded Workshop.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 By the authors