ON THE ULTRABORNOLOGICAL PROPERTY OF THE VECTOR-VALUED BOUNDED-FUNCTION SPACE

被引：1

作者：

FERRANDO, JC ^{[1
]}

机构：

[1] UNIV POLITECN VALENCIA,EU INFORMAT,DEPT MATEMAT APLICADA,E-46071 VALENCIA,SPAIN

来源：

MATHEMATICA SCANDINAVICA | 1993年 / 73卷 / 01期

关键词：

D O I：

10.7146/math.scand.a-12461

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If OMEGA is a set, SIGMA a sigma-algebra of subsets of OMEGA and X is a normed space, we show that the space K(SIGMA, X) of all bounded X-countably valued SIGMA-measurable functions on OMEGA endowed with the supremum-norm is ultrabornological if and only if X is ultrabornological. As a consequence, the space l(infinity)(X) of all bounded sequences in X with the supremum-norm is ultrabornological if and only if X is ultrabornological.

引用

页码：156 / 160

页数：5

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