The transfer of property (β) of rolewicz by a uniform quotient map

S. J. Dilworth, Denka Kutzarova, N. Lovasoa Randrianarivony

Research output: Contribution to journalArticlepeer-review

Abstract

We provide a Laakso construction to prove that the property of having an equivalent norm with the property (β) of Rolewicz is qualitatively preserved via surjective uniform quotient mappings between separable Banach spaces. On the other hand, we show that the (β)-modulus is not quantita- tively preserved via such a map by exhibiting two uniformly homeomorphic Banach spaces that do not have (β)-moduli of the same power type even under renorming.

Original languageEnglish (US)
Pages (from-to)6253-6270
Number of pages18
JournalTransactions of the American Mathematical Society
Volume368
Issue number9
DOIs
StatePublished - Jan 1 2016

Keywords

  • Laakso construction
  • Lipschtiz quotient
  • Property (β) of Rolewicz
  • Uniform quotient

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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