Real Banach spaces with numerical index 1

被引：39

作者：

López, G ^{[1
]}

Martín, M ^{[1
]}

Payá, R ^{[1
]}

机构：

[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada, Spain

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 1999年 / 31卷

关键词：

D O I：

10.1112/S002460939800513X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that an infinite-dimensional real Banach space with numerical index 1 satisfying the Radon-Nikodym property contains II. It follows that a reflexive or quasi-reflexive real Banach space cannot be re-normed to have numerical index 1, unless it is finite-dimensional.

引用

页码：207 / 212

页数：6

共 13 条

[1]

[Anonymous], 1985, GRADUATE TEXTS MATH

[2]

[Anonymous], 1977, MATH SURVEYS

[3]

Bonsall F., 1973, London Mathematical Society Lecture Note Series, V10

[4]

Bonsall F., 1971, London Math. Soc. Lecture Note Series, V2

[5]

BOURGIN RD, 1983, LECT NOTES MATH, V993

[6]

DUNCAN J, 1970, J LONDON MATH SOC, V2, P481

[7]

Fonf V. P., 1979, FUNCT ANAL APPL, V13, P66

[8] INTERSECTION PROPERTIES OF BALLS AND SUBSPACES IN BANACH-SPACES [J].

LIMA, A .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 227 (MAR) :1-62

[9] EXTREME POINT PROPERTIES OF CONVEX BODIES IN REFLEXIVE BANACH SPACES [J].

LINDENSTRAUSS, J ;

PHELPS, RR .

ISRAEL JOURNAL OF MATHEMATICS, 1968, 6 (01) :39-+

[10]

LINDERSTRAUSS J, 1964, MEM AM MATH SOC, V48

← 1 2 →