Research output: Contribution to journal › Article › peer-review
We consider the class AΓ of n-dimensional normed spaces with unit balls of the form: BU = conv ∪ γ∈Γ γ(Bn 1∪U (Bn 1)), where Bn 1 is the unit ball of ℓn 1, Γ is a finite group of orthogonal operators acting in ℝn, and U is a "random" orthogonal transformation. It is proved that this class contains spaces with a large Banach-Mazur distance between them. If the cardinality of Γ is of order nc, it is shown that, in the power scale, the diameter of AΓ in the modified Banach-Mazur distance behaves as the classical diameter and is of order n. Bibliography: 8 titles.
Original language | English |
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Pages (from-to) | 1526-1530 |
Number of pages | 5 |
Journal | Journal of Mathematical Sciences |
Volume | 141 |
Issue number | 5 |
DOIs | |
State | Published - 1 Mar 2007 |
ID: 34905915