Exploration of indispensable Banach-space valued functions

被引：0
|
作者：
Hu, Yiheng [1 ]
Lyu, Gang [1 ]
Jin, Yuanfeng [2 ]
Liu, Qi [3 ]
机构：
[1] Guangzhou Coll Technol & Business, Sch Gen Educ, Guangzhou 510850, Peoples R China
[2] Yanbian Univ, Dept Math, Yanji 133001, Peoples R China
[3] Anqing Normal Univ, Sch Math & Phys, Anqing 246001, Peoples R China
来源：
AIMS MATHEMATICS | 2023年 / 8卷 / 11期
基金：
中国国家自然科学基金;
关键词：
essential bounded Banach-valued function; sequential compactness; uniform convergence;
D O I：
10.3934/math.20231416
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper, we present a necessary and sufficient condition for the existence of a sequence of measurable functions with finite values, which converge to any given essential bounded function in the topology of essential supremum in a Banach space. A new convergence method is proposed, which allows for the discovery of an essential bounded function F that is valued in a Banach space. Generally speaking, there exists a Banach-valued essential bounded function F which Fn can't converge to F in the topology of essential supremum for any sequence of finite-valued measurable function.
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页码：27670 / 27683
页数：14
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