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Extremally distant normed spaces with additional restrictions. / Bakharev, F. L.

In: Mathematical Notes, Vol. 79, No. 3-4, 01.03.2006, p. 314-326.

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

Harvard

Bakharev, FL 2006, 'Extremally distant normed spaces with additional restrictions', Mathematical Notes, vol. 79, no. 3-4, pp. 314-326. https://doi.org/10.1007/s11006-006-0036-4

APA

Bakharev, F. L. (2006). Extremally distant normed spaces with additional restrictions. Mathematical Notes, 79(3-4), 314-326. https://doi.org/10.1007/s11006-006-0036-4

Vancouver

Bakharev FL. Extremally distant normed spaces with additional restrictions. Mathematical Notes. 2006 Mar 1;79(3-4):314-326. https://doi.org/10.1007/s11006-006-0036-4

Author

Bakharev, F. L. / Extremally distant normed spaces with additional restrictions. In: Mathematical Notes. 2006 ; Vol. 79, No. 3-4. pp. 314-326.

BibTeX

@article{a0b3a922a3744e89aa72d2cdb3428bec,
title = "Extremally distant normed spaces with additional restrictions",
abstract = "We study the relationship between the Banach-Mazur distance and the modified Banach-Mazur distance. We sharpen the Szarek theorem on the construction of invariant norms with specific properties and construct extremally distant normed spaces with norms invariant under groups of automorphisms of small cardinality. We prove that the trivial upper bound for the Banach-Mazur distance obtained in terms of the modified Banach-Mazur distance is order-sharp.",
keywords = "Banach space, Banach-Mazur distance, Invariant norm, Modified Banach-Mazur distance, Normed space, Random variable, Symmetry group, Upper bound",
author = "Bakharev, {F. L.}",
year = "2006",
month = mar,
day = "1",
doi = "10.1007/s11006-006-0036-4",
language = "English",
volume = "79",
pages = "314--326",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "3-4",

}

RIS

TY - JOUR

T1 - Extremally distant normed spaces with additional restrictions

AU - Bakharev, F. L.

PY - 2006/3/1

Y1 - 2006/3/1

N2 - We study the relationship between the Banach-Mazur distance and the modified Banach-Mazur distance. We sharpen the Szarek theorem on the construction of invariant norms with specific properties and construct extremally distant normed spaces with norms invariant under groups of automorphisms of small cardinality. We prove that the trivial upper bound for the Banach-Mazur distance obtained in terms of the modified Banach-Mazur distance is order-sharp.

AB - We study the relationship between the Banach-Mazur distance and the modified Banach-Mazur distance. We sharpen the Szarek theorem on the construction of invariant norms with specific properties and construct extremally distant normed spaces with norms invariant under groups of automorphisms of small cardinality. We prove that the trivial upper bound for the Banach-Mazur distance obtained in terms of the modified Banach-Mazur distance is order-sharp.

KW - Banach space

KW - Banach-Mazur distance

KW - Invariant norm

KW - Modified Banach-Mazur distance

KW - Normed space

KW - Random variable

KW - Symmetry group

KW - Upper bound

UR - http://www.scopus.com/inward/record.url?scp=33646012945&partnerID=8YFLogxK

U2 - 10.1007/s11006-006-0036-4

DO - 10.1007/s11006-006-0036-4

M3 - Article

AN - SCOPUS:33646012945

VL - 79

SP - 314

EP - 326

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 3-4

ER -

ID: 34906092