On some properties of Levy vectors and their variations

被引：0
|
作者：
Klinga, Pawel [1 ]
Nowik, Andrzej [1 ]
机构：
[1] Univ Gdansk, Inst Math, Wita Stwosza 57, PL-80952 Gdansk, Poland
来源：
LITHUANIAN MATHEMATICAL JOURNAL | 2023年 / 63卷 / 02期
关键词：
Levy vectors; vector series; Levy-Steinitz theorem; rearrangement of terms; conditionally convergent series; CONVERGENT SERIES;
D O I：
10.1007/s10986-023-09593-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate some properties of Levy vectors of vector series sigma(n is an element of omega) v(n). We consider a generalization of an example from [P. Klinga, Rearranging series of vectors on a small set, J. Math. Anal. Appl., 424(2):966-974, 2015] proving that for a special class of vector series, there exists a subseries that has no convergent subseries with the sum range equal to the plane. To prove this result, we introduce a useful notion of a Levy supervector and prove some of its properties.
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页码：181 / 189
页数：9
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