Asymptotic geometry of banach spaces and uniform quotient maps

S. J. Dilworth, Denka Kutzarova, G. Lancien, N. L. Randrianarivony

Research output: Contribution to journalArticlepeer-review


Recently, Lima and Randrianarivony pointed out the role of the property (β) of Rolewicz in nonlinear quotient problems and answered a tenyear-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.

Original languageEnglish (US)
Pages (from-to)2747-2762
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number8
StatePublished - Aug 1 2014

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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