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 language||English (US)|
|Number of pages||11|
|Journal||Electronic Research Announcements in Mathematical Sciences|
|State||Published - 2012|
All Science Journal Classification (ASJC) codes
- Locally decodable codes
- Projective tensor product