Diameter 2 properties and convexity

被引：19

作者：

Abrahamsen, Trond Arnold ^{[1
]}

Hajek, Petr ^{[2
,3
]}

Nygaard, Olav ^{[1
]}

Talponen, Jarno ^{[4
]}

Troyanski, Stanimir ^{[5
,6
]}

机构：

[1] Univ Agder, Dept Math, Postbox 422, N-4604 Kristiansand, Norway

[2] Acad Sci Czech Republic, Math Inst, Zitna 25, CR-11567 Prague 1, Czech Republic

[3] Czech Tech Univ, Fac Elect Engn, Dept Math, Zikova 4, Prague, Czech Republic

[4] Univ Eastern Finland, Dept Math & Phys, Box 111, FI-80101 Joensuu, Finland

[5] Univ Murcia, Dept Matemat, Campus Espinardo, Espinardo 30100, Murcia, Spain

[6] Bulgarian Acad Sci, Inst Math & Informat, Bl 8,Acad G Bonchev St, BU-1113 Sofia, Bulgaria

来源：

STUDIA MATHEMATICA | 2016年 / 232卷 / 03期

基金：

芬兰科学院;

关键词：

diameter; 2; property; midpoint locally uniformly rotund; Daugavet property; WEAKLY OPEN SUBSETS; BANACH-SPACES; M-IDEALS; SLICES;

D O I：

10.4064/sm8317-4-2016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present an equivalent midpoint locally uniformly rotund (MLUR) renorming of C[0, 1] with the diameter 2 property (D2P), i.e. every non-empty relatively weakly open subset of the unit ball has diameter 2. An example of an MLUR space with the D2P and with convex combinations of slices of arbitrarily small diameter is also given.

引用

页码：227 / 242

页数：16

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