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Estimates of maximal distances between spaces whose norms are invariant under a group of operators. / Bakharev, F. L.

In: Journal of Mathematical Sciences, Vol. 141, No. 5, 01.03.2007, p. 1526-1530.

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

Harvard

Bakharev, FL 2007, 'Estimates of maximal distances between spaces whose norms are invariant under a group of operators', Journal of Mathematical Sciences, vol. 141, no. 5, pp. 1526-1530. https://doi.org/10.1007/s10958-007-0058-9

APA

Bakharev, F. L. (2007). Estimates of maximal distances between spaces whose norms are invariant under a group of operators. Journal of Mathematical Sciences, 141(5), 1526-1530. https://doi.org/10.1007/s10958-007-0058-9

Vancouver

Bakharev FL. Estimates of maximal distances between spaces whose norms are invariant under a group of operators. Journal of Mathematical Sciences. 2007 Mar 1;141(5):1526-1530. https://doi.org/10.1007/s10958-007-0058-9

Author

Bakharev, F. L. / Estimates of maximal distances between spaces whose norms are invariant under a group of operators. In: Journal of Mathematical Sciences. 2007 ; Vol. 141, No. 5. pp. 1526-1530.

BibTeX

@article{3b9b8505d3d34384b2ef7d1afbdd3d7c,
title = "Estimates of maximal distances between spaces whose norms are invariant under a group of operators",
abstract = "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.",
author = "Bakharev, {F. L.}",
year = "2007",
month = mar,
day = "1",
doi = "10.1007/s10958-007-0058-9",
language = "English",
volume = "141",
pages = "1526--1530",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "5",

}

RIS

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