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

2014/08/27 by S. J. Dilworth, Dilworth, S. J., Denka Kutzarova +3
Mathematics · #46B20 (Primary) #46B80 #46T99 #51F99 (Secondary) #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1408.6424

openalex publication_date 2014/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Property (β) and uniform quotient maps
• Equivalent norms with the property (β) of Rolewicz
• An asymptotic analog of a local-to-global phenomenon for uniformly convex renormings
• Asymptotic geometry of Banach spaces and uniform quotient maps
• A submetric characterization of Rolewicz's property (β)