EMBEDDING NORMED LINEAR SPACES INTO C(X)

被引：0

作者：

Fakhar, M. ^{[1
,2
]}

Koushesh, M. R. ^{[2
,3
]}

Raoofi, M. ^{[1
]}

机构：

[1] Univ Isfahan, Dept Math, Esfahan 81745163, Iran

[2] IPM, Sch Math, Inst Res Fundamental Sci, POB 19395-5746, Tehran, Iran

[3] Isfahan Univ Technol, Dept Math, Esfahan 8415683111, Iran

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2017年 / 43卷 / 01期

关键词：

Stone-Cech compactification; Banach-Alaoglu theorem; embedding theorem;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that every (real or complex) normed linear space L is isometrically embeddable into C(X) for some compact Hausdorff space X. Here X is the closed unit ball of L* (the set of all continuous scalar-valued linear mappings on L) endowed with the weak* topology, which is compact by the Banach Alaoglu theorem. We prove that the compact Hausdorff space X can indeed be chosen to be the Stone-Caech compactification of L* \ {0}, where L* \ {0} is endowed with the supremum norm topology.

引用

页码：131 / 135

页数：5

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