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arXiv · 1408.6424

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

S. J. Dilworth·Denka Kutzarova·N. Lovasoa Randrianarivony
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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 quantitatively 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.

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S. J. Dilworth, Denka Kutzarova, N. Lovasoa Randrianarivony. 2014-08-27. The transfer of property $(β)$ of Rolewicz by a uniform quotient map. https://arxiv.org/abs/1408.6424

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