A SOLUTION TO BANACHS HYPERPLANE PROBLEM

被引：66

作者：

GOWERS, WT

机构：

[1] Department of Mathematics, University College, London, WC1E 6BT, Gower Street

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 1994年 / 26卷

关键词：

D O I：

10.1112/blms/26.6.523

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An infinite-dimensional Banach space X is constructed which is not isomorphic to X + R. Equivalently, X is not isomorphic to any of its closed subspaces of codimension one. This gives a negative answer to a question of Banach. In fact, X has the stronger property that it is not isomorphic to any proper subspace. It also happens to have an unconditional basis.

引用

页码：523 / 530

页数：8

共 12 条

[1]

Banach S., 1932, THEORIE OPERATIONS L

[2]

BESSAGA G, 1958, STUD MATH, V17, P165

[3]

FIGIEL T, 1974, COMPOS MATH, V29, P179

[4]

GASAZZA PG, HANDWRITTEN NOTES