Some nonlinear characterizations of reflexive Banach spaces
发布时间：2024-10-25
点击次数：
影响因子：1.3
DOI码：10.1016/j.jmaa.2022.126736
发表刊物：J. Math. Anal. Appl.
关键字：Reflexive Banach spaces inf–convolution James theorem Lower semicontinuous convex coercive function Sequentially weakly lower semicontinuous coercive function Attainment of infima
摘要：It is well known that in the calculus of variations and in optimization there exist many formulations of the fundamental propositions on the attainment of the infima of sequentially weakly lower semicontinuous coercive functions on reflexive Banach spaces. By either some constructive skills or the regularization skill by inf–convolutions we show in this paper that all these formulations together with their important variants are equivalent to each other and equivalent to the reflexivity of the underlying space. Motivated by this research, we also give a characterization for a normed space to be finite dimensional: a normed space is finite dimensional iff every continuous real–valued function defined on each bounded closed subset of this space can attain its minimum, namely the converse of the classical Weierstrass theorem also holds true.
合写作者：Shiqing Zhang, Tiexin Guo
第一作者：Yan Tang
论文类型：期刊论文
论文编号：126736
学科门类：理学
一级学科：数学
文献类型：J
卷号：519
ISSN号：0022-247X
是否译文：否
发表时间：2022-09-30
收录刊物：SCI
发布期刊链接：https://www.sciencedirect.com/science/article/pii/S0022247X22007508?via%3Dihub