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.

引用

页码：348 / 362

页数：15

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