DIAMOND GRAPHS AND SUPER-REFLEXIVITY Academic Article uri icon

abstract

  • The main result is that a Banach space X is not super-reflexive if and only if the diamond graphs D n Lipschitz embed into X with distortions independent of n. One of the consequences of that and previously known results is that dimension reduction a la JohnsonLindenstrauss fails in any non-super-reflexive space with nontrivial type. We also introduce the concept of Lipschitz (p,r)-summing map and prove that every Lipschitz mapping is Lipschitz (p,r)-summing for every 1 ≤ r < p. © 2009 World Scientific Publishing Company.

author list (cited authors)

  • JOHNSON, W. B., & SCHECHTMAN, G.

citation count

  • 26

complete list of authors

  • JOHNSON, WILLIAM B||SCHECHTMAN, GIDEON

publication date

  • June 2009