THICKNESS OF THE UNIT SPHERE, l1-TYPES, AND THE ALMOST DAUGAVET PROPERTY

被引：0

作者：

Kadets, Vladimir ^{[1
]}

Shepelska, Varvara ^{[1
]}

Werner, Dirk ^{[2
]}

机构：

[1] Kharkov Natl Univ, Dept Mech & Math, UA-61077 Kharkov, Ukraine

[2] Univ Berlin, Dept Math, D-14195 Berlin, Germany

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2011年 / 37卷 / 03期

关键词：

Daugavet property; l(1)-subspace; types; thickness; BANACH-SPACES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study those Banach spaces X for which S-X does not admit a finite epsilon-net consisting of elements of S-X for any epsilon < 2. We give characterisations of this class of spaces in terms of l(1)-type sequences and in terms of the almost Daugavet property. The main result of the paper is: a separable Banach space X is isomorphic to a space from this class if and only if X contains an isomorphic copy of l(1).

引用

页码：867 / 878

页数：12

共 16 条

[1] The polynomial Daugavet property for atomless L1(μ)-spaces
Martin, Miguel
Meri, Javier
Popov, Mikhail
ARCHIV DER MATHEMATIK, 2010, 94 (04) : 383 - 389
[2] The polynomial Daugavet property for atomless L1(μ)-spaces
Miguel Martín
Javier Merí
Mikhail Popov
Archiv der Mathematik, 2010, 94 : 383 - 389
[3] Weak Neighborhoods and the daugavet property of the interpolation spaces L1+L∞ and L1 ∧ L∞
Acosta, Maria D.
Kaminska, Anna
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (01) : 77 - 96
[4] An approximation property and the sphere of L1
Wulbert, D
JOURNAL OF APPROXIMATION THEORY, 1999, 101 (01) : 160 - 163
[5] ON LINEAR-DIFFERENTIAL EQUATIONS WITH ALMOST PERIODIC COEFFICIENTS AND THE PROPERTY THAT THE UNIT-SPHERE IS INVARIANT
KURZWEIL, J
VENCOVSKA, A
LECTURE NOTES IN MATHEMATICS, 1983, 1017 : 364 - 368
[6] ALMOST ISOMETRIES ON THE UNIT BALL OF L1
LOVBLOM, GM
ISRAEL JOURNAL OF MATHEMATICS, 1988, 63 (02) : 129 - 138
[7] Lacunary polynomials in L1: Geometry of the unit sphere
Dyakonov, Konstantin M.
ADVANCES IN MATHEMATICS, 2021, 381
[8] The isometric extension of an into mapping from the unit sphere S(l∞(2)) to S(L1(μ))
Ding, Guang Gui
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2006, 22 (06) : 1721 - 1724
[9] ISOMETRIES ON THE UNIT SPHERE OF THE l1-SUM OF STRICTLY CONVEX NORMED SPACES
Li, Lei
ANNALS OF FUNCTIONAL ANALYSIS, 2016, 7 (01): : 33 - 41
[10] On the quasi-Figiel problem and extension of ε-isometry on unit sphere of L∞,1+ space
Liu, Rui
Yin, Jifu
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 525 (02)

← 1 2 →