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

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.