[1]鲍玲鑫,施慧华.A-收敛与几乎处处收敛[J].华侨大学学报(自然科学版),2015,36(6):726-730.[doi:10.11830/ISSN.1000-5013.2015.06.0726]
　BAO Lingxin,SHI Huihua.On A-Convergence and Almost Usual Convergence[J].Journal of Huaqiao University(Natural Science),2015,36(6):726-730.[doi:10.11830/ISSN.1000-5013.2015.06.0726]
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A-收敛与几乎处处收敛()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第36卷
期数:
2015年第6期
页码:
726-730
栏目:
出版日期:
2015-11-10

文章信息/Info

Title:
On A-Convergence and Almost Usual Convergence
文章编号:
1000-5013(2015)06-0726-05
作者:
鲍玲鑫1;  施慧华2
1. 福建农林大学 计算机与信息学院, 福建 福州 350002;2. 华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
BAO Lingxin1;  SHI Huihua2
1. School of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou 350002, China; 2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
统计收敛;  理想收敛;  几乎处处收敛;  极端测度;  Banach空间
Keywords:
statistical convergence;  ideal convergence;  almost usual convergence;  extreme measures;  Banach space
分类号:
O177.2
DOI:
10.11830/ISSN.1000-5013.2015.06.0726
文献标志码:
A
摘要:
设A≡(ai)∞i=1?S</sup>+<sub>l1,其中,S</sup>+<sub>l1表示l1单位球面上的所有正向量构成的集合.Banach空间X中的序列(xn)称为A-收敛于x∈X,是指对任意的ε&gt;0,limi→∞〈ai,χA(ε)〉=0,其中,A(ε)={n∈N∶‖xn-x‖≥ε}.用两种不同的收敛方式刻画A-收敛,即证明对任意A≡(ai)∞i=1?S</sup>+<sub>l1,存在一个N上的理想IA,以及一族极端有限可加概率测度Pext(IA),使A-收敛且理想IA-收敛和测度Pext(IA)-收敛互为等价.此外,证明A-收敛为测度Pext(IA)-几乎处处收敛的充分必要条件是该A-收敛为非退化的.
Abstract:
Let A≡(ai)∞i=1?S+l1, a sequence(xn)of points in a Banach X is said to be A-convergent to x∈X provided that for any ε&gt;0, limi→∞〈ai,χA(ε)〉=0,where A(ε)={n∈N∶‖xn-x‖≥ε}. In this paper, we give two different approaches of A-convergence via ideal on N and via extreme measures. We show that for any A≡(ai)∞i=1?S+l1, there exist an ideal IA and a collection Pext(IA)of extreme probability measures such that the A-convergence, the ideal IA-convergence and the measure Pext(IA)-convergence are equivalent. We also show that A-convergence equivalent to Pext(IA)-almost usual convergence if and only if it is nondegenerate.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2015-04-03
通信作者: 鲍玲鑫(1982-),男,讲师,博士,主要从事基础数学泛函分析、Banach空间几何的研究.E-mail:bolingxmu@sina.com.
基金项目: 国家自然科学基金专项数学天元基金资助项目(11426064, 11426061); 国家自然科学基金青年基金资助项目(11401227, 11501108); 福建省自然科学基金资助项目(2015J01579)
更新日期/Last Update: 2015-11-20