LIMIT SETS IN NORMED LINEAR SPACES

被引：1

作者：

Charatonik, Wlodzimierz J. ^{[1
]}

Samulewicz, Alicja ^{[2
]}

Witula, Roman ^{[2
]}

机构：

[1] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA

[2] Silesian Tech Univ, Fac Appl Math, Inst Math, Kaszubska 23, PL-44101 Gliwice, Poland

来源：

COLLOQUIUM MATHEMATICUM | 2017年 / 147卷 / 01期

关键词：

normed space; limit point; series; VECTOR SERIES; REARRANGEMENTS; THEOREM;

D O I：

10.4064/cm6868-5-2016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The sets of all limit points of series with terms tending to 0 in normed linear spaces are characterized. An immediate conclusion is that a normed linear space (X, parallel to.parallel to) is infinite-dimensional if and only if there exists a series Sigma x(n) of terms of X with x(n) -> 0 whose set of limit points contains exactly two different points of X. The last assertion could be extended to an arbitrary (greater than 1) finite number of points.

引用

页码：35 / 42

页数：8

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[21] COMPLETION OF NORMED LINEAR SPACES
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[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 19 (04) : 801 - &
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[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 69 (JUL) : 89 - 108
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[26] ON ISOMETRIES OF NORMED LINEAR SPACES
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[J]. STUDIA MATHEMATICA, 1970, 36 (03) : 213 - &
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