Minkowski spaces with extremal distance from the Euclidean space

Vitali Milman; H. Wolfson

doi:10.1007/BF02762002

Minkowski spaces with extremal distance from the Euclidean space

Vitali Milman^*, H. Wolfson

^*Corresponding author for this work

Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

It is proved that if the Banach-Mazur distance between an n-dimensional Minkowski space B and l₂ⁿ satisfies d (B₁ l₂ⁿ ) ≧c √n (for some constant c>0 and for big n) then B contains an A(c)-isomorphic copy of l₁^k (for k ∼ log log log n). In the special case d (B₁ l₂ⁿ ) = √n, B contains an isometric copy of l₁^k for k ∼ log n.

Original language	English
Pages (from-to)	113-131
Number of pages	19
Journal	Israel Journal of Mathematics
Volume	29
Issue number	2-3
DOIs	https://doi.org/10.1007/BF02762002
State	Published - Jun 1978

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title = "Minkowski spaces with extremal distance from the Euclidean space",

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.",

author = "Vitali Milman and H. Wolfson",

year = "1978",

month = jun,

doi = "10.1007/BF02762002",

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AU - Wolfson, H.

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N2 - 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.

AB - 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.

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

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ER -

Minkowski spaces with extremal distance from the Euclidean space

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