2015/12/31 by Bruno de Mendonça Braga, Bruno M. Braga
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Banach manifold #Banach space #Computer science #Discrete mathematics #Embedding #Geometry #Holomorphic and Operator Theory #Infinite-dimensional vector function #Inverse #Lp space #Mathematical analysis #Mathematics #Order (exchange) #Pure mathematics #Relation (database) #Space (punctuation) #Uniformly convex space #math.FA #msc:46B80
paper · pdf · doi:10.1016/j.jfa.2016.12.005
in Journal of Functional Analysis (2017)
openalex publication_date 2016/12/16 · arxiv created 2016/12/22 · arxiv updated 2016/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In these notes, we study the relation between uniform and coarse embeddings between Banach spaces. In order to understand this relation better, we also look at the problem of when a coarse embedding can be assumed to be topological. Among other results, we show that if a Banach space X uniformly embeds into a minimal Banach space Y, then X simultaneously coarsely and uniformly embeds into Y, and if a Banach space X coarsely embeds into a minimal Banach space Y, then X simultaneously coarsely and homeomorphically embeds into Y by a map with uniformly continuous inverse.