Published 2006
| Published
Journal Article
Open
Some applications of Ball's extension theorem
- Creators
- Mendel, Manor
- Naor, Assaf
Abstract
We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type 2 problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice {0,1,...,m}^n, equipped with the ℓ_p^n metric, in any 2-uniformly convex Banach space is of order min {n^(1/2 1/p),m^(1-2/p)}.
Additional Information
© 2006 American Mathematical Society. Article electronically published on February 17, 2006. Received by the editors January 27, 2005 and, in revised form, March 18, 2005. Communicated by: David Preiss.Attached Files
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Additional details
- Eprint ID
- 24553
- Resolver ID
- CaltechAUTHORS:20110726-141906874
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2011-07-27Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field