A note on the Banach-Mazur problem

被引：6

作者：

Randrianantoanina, B ^{[1
]}

机构：

[1] Miami Univ, Dept Math & Stat, Oxford, OH 45056 USA

来源：

GLASGOW MATHEMATICAL JOURNAL | 2002年 / 44卷

关键词：

D O I：

10.1017/S001708950201011X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if X is a real Banach space, with dim X greater than or equal to 3, which contains subspace of codimension I which is I-complemented in X and whose group of isometries is almost transitive then X is isometric to a Hilbert space. This partially answers the Banach-Mazur rotation problem and generalizes some recent related results.

引用

页码：159 / 165

页数：7

共 50 条

[31] The Banach-Mazur compactum Q*(n) is an AR
Ageev, SM
Bogatyi, SA
Fabel, P
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1998, (01): : 11 - 13
[32] Banach-Mazur game and open mapping theorem
Noll, Dominikus
TOPOLOGY AND ITS APPLICATIONS, 2022, 322
[33] New topological models for Banach-Mazur compacta
Antonyan S.A.
Journal of Mathematical Sciences, 2007, 146 (1) : 5465 - 5473
[34] The *-variation of the Banach-Mazur game and forcing axioms
Yoshinobu, Yasuo
ANNALS OF PURE AND APPLIED LOGIC, 2017, 168 (06) : 1335 - 1359
[35] The Banach-Mazur game and sigma-porosity
Zeleny, M
FUNDAMENTA MATHEMATICAE, 1996, 150 (03) : 197 - 210
[36] The Banach-Mazur theorem for spaces with an asymmetric distance
Alimov, AR
RUSSIAN MATHEMATICAL SURVEYS, 2003, 58 (02) : 367 - 369
[37] BANACH-MAZUR DISTANCE BETWEEN CONVEX QUADRANGLES
Lassak, Marek
DEMONSTRATIO MATHEMATICA, 2014, 47 (04) : 989 - 993
[38] Generalized volume ratios and the Banach-Mazur distance
Khrabrov, AI
MATHEMATICAL NOTES, 2001, 70 (5-6) : 838 - 846
[39] GENERALIZED BANACH-MAZUR FUNCTIONALS IN THE TOPOS OF RECURSIVE SETS
MULRY, PS
JOURNAL OF PURE AND APPLIED ALGEBRA, 1982, 26 (01) : 71 - 83
[40] On Banach space properties that are not invariant under the Banach-Mazur distance 1
Piasecki, Lukasz
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 467 (02) : 1129 - 1147

← 1 2 3 4 5 →