NEW RESULTS ON KOTTMAN'S CONSTANT

被引：8
|
作者：
Castillo, Jesus M. F. [1 ]
Gonzalez, Manuel [2 ]
Papini, Pier Luigi [3 ]
机构：
[1] Univ Extremadura, Dept Matemat, Ave Elvas S-N, E-06071 Badajoz, Spain
[2] Univ Cantabria, Dept Matemat, Ave Castros S-N, Santander 39071, Spain
[3] Via Martucci 19, I-40136 Bologna, Italy
来源：
BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2017年 / 11卷 / 02期
关键词：
Kottman's constant; Banach space; twisted Hilbert spaces; BANACH-SPACES; SEPARATED SEQUENCES; REFLEXIVITY; CONVEXITY; BALL;
D O I：
10.1215/17358787-0000007X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present new results on Kottman's constant of a Banach space, showing (i) that every Banach space is isometric to a hyperplane of a Banach space having Kottman's constant 2 and (ii) that Kottman's constant of a Banach space and of its bidual can be different. We say that a Banach space is a Diestel space if the infimum of Kottman's constants of its subspaces is greater that 1. We show that every Banach space contains a Diestel subspace and that minimal Banach spaces are Diestel spaces.
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页码：348 / 362
页数：15
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