Measures of weak non-compactness in l1()-spaces
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY(2023)
摘要
Disjoint sequence methods from the theory of Riesz spaces areused to study measures of weak non-compactness inL1(mu)-spaces. A principalnew result of the present paper is the following: LetEbe an abstractM-space.Then omega(B)=sup{lim supn ->infinity rho B(xn):(xn)n subset of BEdisjoint} =inf{epsilon>0:there exists x & lowast;is an element of E & lowast;+so thatB subset of[-x & lowast;,x & lowast;]+epsilon BE & lowast; =sup{lim supn ->infinity rho B(xn):(xn)n subset of BEweakly null =sup{ca rho B((xn)n):(xn)n subset of(BE)+increasing=sup{lim supn ->infinity & Vert;x & lowast;n & Vert;:(x & lowast;n)n subset of Sol(B) disjoint=sup{lim supn ->infinity supx & lowast;is an element of B|< x & lowast;,xn >|:(xn)n subset of BEdisjoint} for every norm bounded subsetBofE & lowast;.
更多查看译文
关键词
Banach lattices,measures of weak non-compactness,abstract L-spaces,abstract M-spaces
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要