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Journal of Mathematical Sciences

, Volume 141, Issue 5, pp 1526–1530 | Cite as

Estimates of maximal distances between spaces whose norms are invariant under a group of operators

  • F. L. Bakharev
Article
  • 15 Downloads

Abstract

We consider the class Aг of n-dimensional normed spaces with unit balls of the form: \(B_U = conv\mathop \cup \limits_{\gamma \in \Gamma } \gamma (B_n^1 \cup U(B_n^1 ))\), where B n 1 n is the unit ball of ℓ n 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 Aг in the modified Banach-Mazur distance behaves as the classical diameter and is of order n. Bibliography: 8 titles.

Keywords

Random Vector Unit Ball Classical Diameter Orthogonal Transformation Polar Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • F. L. Bakharev
    • 1
  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

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