Locally decodable codes and the failure of cotype for projective tensor products
نویسندگان
چکیده
It is shown that for every p ∈ (1,∞) there exists a Banach space X of finite cotype such that the projective tensor product lp⊗̂X fails to have finite cotype. More generally, if p1, p2, p3 ∈ (1,∞) satisfy 1 p1 + 1 p2 + 1 p3 6 1 then lp1⊗̂lp2⊗̂lp3 does not have finite cotype. This is a proved via a connection to the theory of locally decodable codes.
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عنوان ژورنال:
- CoRR
دوره abs/1208.0539 شماره
صفحات -
تاریخ انتشار 2012