DIAMOND GRAPHS AND SUPER-REFLEXIVITY
Academic Article
-
- Overview
-
- Research
-
- Identity
-
- Additional Document Info
-
- View All
-
Overview
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
complete list of authors
-
JOHNSON, WILLIAM B||SCHECHTMAN, GIDEON
publication date
publisher
published in
Research
keywords
-
(p, Q) Summing Operator
-
Diamond Graph
-
Dimension Reduction
-
Super Reflexivity
Identity
Digital Object Identifier (DOI)
Additional Document Info
start page
end page
volume
issue