Minkowski spaces with extremal distance from the Euclidean space

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Abstract

It is proved that if the Banach-Mazur distance between an n-dimensional Minkowski space B and l 2 n satisfies d (B 1 l 2 n ) ≧c √n (for some constant c>0 and for big n) then B contains an A(c)-isomorphic copy of l 1 k (for k ∼ log log log n). In the special case d (B 1 l 2 n ) = √n, B contains an isometric copy of l 1 k for k ∼ log n.

Original languageEnglish
Pages (from-to)113-131
Number of pages19
JournalIsrael Journal of Mathematics
Volume29
Issue number2-3
DOIs
StatePublished - Jun 1978

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