A NEW COARSELY RIGID CLASS OF BANACH SPACES Academic Article uri icon

abstract

  • AbstractWe prove that the class of reflexive asymptotic-$c_{0}$ Banach spaces is coarsely rigid, meaning that if a Banach space $X$ coarsely embeds into a reflexive asymptotic-$c_{0}$ space $Y$, then $X$ is also reflexive and asymptotic-$c_{0}$. In order to achieve this result, we provide a purely metric characterization of this class of Banach spaces. This metric characterization takes the form of a concentration inequality for Lipschitz maps on the Hamming graphs, which is rigid under coarse embeddings. Using an example of a quasi-reflexive asymptotic-$c_{0}$ space, we show that this concentration inequality is not equivalent to the non-equi-coarse embeddability of the Hamming graphs.

published proceedings

  • JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU

altmetric score

  • 1

author list (cited authors)

  • Baudier, F., Lancien, G., Motakis, P., & Schlumprecht, T. h.

citation count

  • 3

complete list of authors

  • Baudier, F||Lancien, G||Motakis, P||Schlumprecht, Th

publication date

  • September 2021