TY - JOUR
T1 - Locally decodable codes and the failure of cotype for projective tensor products
AU - Brië, Jop T.
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
AN - SCOPUS:84873372916
SN - 1935-9179
VL - 19
SP - 120
EP - 130
JO - Electronic Research Announcements in Mathematical Sciences
JF - Electronic Research Announcements in Mathematical Sciences
ER -