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Estimates of maximal distances between spaces whose norms are invariant under a group of operators. / Bakharev, F. L.
в: Journal of Mathematical Sciences, Том 141, № 5, 01.03.2007, стр. 1526-1530.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Estimates of maximal distances between spaces whose norms are invariant under a group of operators
AU - Bakharev, F. L.
PY - 2007/3/1
Y1 - 2007/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33846979141&partnerID=8YFLogxK
U2 - 10.1007/s10958-007-0058-9
DO - 10.1007/s10958-007-0058-9
M3 - Article
AN - SCOPUS:33846979141
VL - 141
SP - 1526
EP - 1530
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 5
ER -
ID: 34905915