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.

引用

页码：27670 / 27683

页数：14

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