[1]施慧华.半范数pA的特征[J].华侨大学学报(自然科学版),2021,42(6):844-848.[doi:10.11830/ISSN.1000-5013.202011040]
　SHI Huihua.Characterization of Semi-Norm pA[J].Journal of Huaqiao University(Natural Science),2021,42(6):844-848.[doi:10.11830/ISSN.1000-5013.202011040]
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半范数pA的特征()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第42卷
期数:
2021年第6期
页码:
844-848
栏目:
出版日期:
2021-11-12

文章信息/Info

Title:
Characterization of Semi-Norm pA
文章编号:
1000-5013(2021)06-0844-05
作者:
施慧华
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
SHI Huihua
School of Mathematics Science, Huaqiao University, Quanzhou 362021, China
关键词:
半范数 pA;  A-收敛;  强无原子次测度;  无原子理想
Keywords:
semi-norm pA;  A-convergence;  strong nonatomic submeasure;  nonatomic ideal
分类号:
O177.2
DOI:
10.11830/ISSN.1000-5013.202011040
文献标志码:
A
摘要:
记A={ai}∞i=1={(ai,j)∞j=1}∞i=1?S+l1,其中,S+l1={x=(x(n))∈l1:‖x‖=1,x(n)≥0,∠n∈N},pA(x)=limi→∞ sup∑j=1ai,j|x(j)|,则limi→∞ Si≡limi→∞supj ai,j=0,当且仅当对任意非空集合B?N,任意0≤β≤pA(χB),均存在C?B,满足pA(χC)=β.对B?N,记φA(B)=pA(χB),证明了φA 的强无原子性当且仅当理想IA={A?N:pA(χA)=0}的无原子性.
Abstract:
Let A={ai}∞i=1={(ai,j)∞j=1}∞i=1?S+l1, where S+l1={x=(x(n))∈l1:‖x‖=1, x(n)≥0, ∠n∈N}, pA(x)=limi→∞ sup ∑j=1ai,j|x(j)|, then limi→∞ Si≡limi→∞ supj ai,j=0, if and only if for any nonempty subset B?N, any 0≤β≤pA(χB), there always exists C?B such that pA(χC)=β. Let φA(B)=pA(χB)for B?N, it is also proved that φA is strong nonatomic if and only if ideal IA={A?N:pA(χA)=0} is nonatomic.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2020-11-19
通信作者: 施慧华(1981-),女,讲师,博士,主要从事基础数学泛函分析的研究.E-mail:shh817@hqu.edu.com.
基金项目: 国家自然科学基金资助项目(11401227, 11226129)
更新日期/Last Update: 2021-11-20