This is an announcement for the paper "The transfer of property $(\beta)$ of Rolewicz by a uniform quotient" by S. J. Dilworth, Denka Kutzarova, and N. Lovasoa Randrianarivony.

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

Archive classification: math.FA math.MG

Mathematics Subject Classification: 46B20 (Primary), 46B80, 46T99, 51F99 (Secondary)

Submitted from: nrandria@slu.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1408.6424

or

http://arXiv.org/abs/1408.6424