DIAMOND GRAPHS AND SUPER-REFLEXIVITY Academic Article

abstract

• The main result is that a Banach space X is not super-reflexive if and only if the diamond graphs Dn 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.

authors

• Johnson, William

published proceedings

• Journal of Topology and Analysis

author list (cited authors)

• JOHNSON, W. B., & SCHECHTMAN, G.

citation count

• 30

complete list of authors

• JOHNSON, WILLIAM B||SCHECHTMAN, GIDEON

publication date

• June 2009

publisher

• World Scientific Pub Co Pte Lt  Publisher

published in

• Journal of Topology and Analysis  Journal

keywords

• (p, Q) Summing Operator
• Diamond Graph
• Dimension Reduction
• Super Reflexivity

Digital Object Identifier (DOI)

• 10.1142/s1793525309000114

start page

• 177

end page

• 189

volume

• 01

issue

• 02