Exploration of indispensable Banach-space valued functions-Reference-Cited by-同舟云学术

Exploration of indispensable Banach-space valued functions

Published:2023 Issue:11 Volume:8 Page:27670-27683
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Hu Yiheng¹,Lyu Gang¹,Jin Yuanfeng²,Liu Qi³

Affiliation:

1. School of General Education, Guangzhou College of Technology and Business, Guangzhou 510850, China

2. Department of Mathematics, Yanbian University, Yanji 133001, China

3. School of Mathematics and Physics, Anqing Normal University, Anqing 246001, China

Abstract

<abstract><p>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 $ F_n $ can't converge to $ F $ in the topology of essential supremum for any sequence of finite-valued measurable function.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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