Locally decodable codes and the failure of cotype for projective tensor products

JopT Brië, Assaf Naor, Oded Regev

Research output: Contribution to journalArticle

Abstract

It is shown that for every p ε (1, ∞) there exists a Banach space X of finite cotype such that the projective tensor product ℓpX fails to have finite cotype. More generally, if p1, p2,p3 ε (1,∞) satisfy 1/p1+1/p2+1/p3 ≤ 1 then lp1lp2p3 does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.

Original languageEnglish (US)
Pages (from-to)120-130
Number of pages11
JournalElectronic Research Announcements in Mathematical Sciences
Volume19
DOIs
StatePublished - 2012

Fingerprint

Tensor Product
Banach space

Keywords

  • Cotype
  • Locally decodable codes
  • Projective tensor product

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Locally decodable codes and the failure of cotype for projective tensor products. / Brië, JopT; Naor, Assaf; Regev, Oded.

In: Electronic Research Announcements in Mathematical Sciences, Vol. 19, 2012, p. 120-130.

Research output: Contribution to journalArticle

@article{6e9dcc68b0f44dfc8fa1161e7521470d,
title = "Locally decodable codes and the failure of cotype for projective tensor products",
abstract = "It is shown that for every p ε (1, ∞) there exists a Banach space X of finite cotype such that the projective tensor product ℓpX fails to have finite cotype. More generally, if p1, p2,p3 ε (1,∞) satisfy 1/p1+1/p2+1/p3 ≤ 1 then lp1lp2p3 does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.",
keywords = "Cotype, Locally decodable codes, Projective tensor product",
author = "JopT Bri{\"e} and Assaf Naor and Oded Regev",
year = "2012",
doi = "10.3934/era.2012.19.120",
language = "English (US)",
volume = "19",
pages = "120--130",
journal = "Electronic Research Announcements in Mathematical Sciences",
issn = "1935-9179",
publisher = "American Mathematical Society",

}

TY - JOUR

T1 - Locally decodable codes and the failure of cotype for projective tensor products

AU - Brië, JopT

AU - Naor, Assaf

AU - Regev, Oded

PY - 2012

Y1 - 2012

N2 - It is shown that for every p ε (1, ∞) there exists a Banach space X of finite cotype such that the projective tensor product ℓpX fails to have finite cotype. More generally, if p1, p2,p3 ε (1,∞) satisfy 1/p1+1/p2+1/p3 ≤ 1 then lp1lp2p3 does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.

AB - It is shown that for every p ε (1, ∞) there exists a Banach space X of finite cotype such that the projective tensor product ℓpX fails to have finite cotype. More generally, if p1, p2,p3 ε (1,∞) satisfy 1/p1+1/p2+1/p3 ≤ 1 then lp1lp2p3 does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.

KW - Cotype

KW - Locally decodable codes

KW - Projective tensor product

UR - http://www.scopus.com/inward/record.url?scp=84873372916&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873372916&partnerID=8YFLogxK

U2 - 10.3934/era.2012.19.120

DO - 10.3934/era.2012.19.120

M3 - Article

VL - 19

SP - 120

EP - 130

JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

SN - 1935-9179

ER -