CONTINUOUS-SELECTIONS AND STABLE RANK OF BANACH-ALGEBRAS

被引：5

作者：

CORACH, G ^{[1
]}

SUAREZ, FD ^{[1
]}

机构：

[1] INST ARGENTINO MATEMAT,RA-1053 BUENOS AIRES,ARGENTINA

来源：

TOPOLOGY AND ITS APPLICATIONS | 1992年 / 43卷 / 03期

关键词：

BANACH ALGEBRA; STABLE RANK; CONTINUOUS SELECTION; DIMENSION;

D O I：

10.1016/0166-8641(92)90159-W

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a paracompact space and A a (real or complex) Banach algebra. The main result of this paper is that the (Bass) stable rank of C(X, A), the algebra of all maps from X into A, is at most the stable rank of A plus the dimension of X. The result extends a previous one of Corach and Larotonda, valid for X compact. The present proof is based on Michael's theory of selections. Using the same techniques we obtain additional theorems improving the inequality and giving some information on the topology of the spaces of unimodular vectors in A(n).

引用

页码：237 / 248

页数：12

共 16 条

[1]

Bass H., 1964, PUBL IHES, V22, P489

[2] A STABILIZATION-THEOREM FOR BANACH-ALGEBRAS [J].